1.  To derive the Engel curve, which shows the relationship between the quantity of a good consumed and a consumer’s income, all else equal, solve the consumer’s:  
A)  utilitymaximization problem with prices of the goods as variables while keeping income constant.  
B)  utilitymaximization problem with income as a variable while keeping the prices of the goods constant.  
C)  expenditureminimization problem with prices of the goods as variables while keeping income constant.  
D)  expenditureminimization problem with income as a variable while keeping the prices of the goods constant. 
2.  We can use the calculus of the consumer choice model for each of the following EXCEPT:  
A)  to see how the demand curve shifts when there is a discrete change in income or the price of the other good.  
B)  to see how the demand curve shifts when tastes for a good change.  
C)  to see how the supply curve shifts when tastes for a good change.  
D)  to see the effects of a change in price of the good itself. 
3.  Suppose that Bella’s utility function from bananas (B) and chocolate (C) is
Her budget is $15, and the price of chocolate is $3. a. Derive Bella’s demand for bananas. b. Suppose that Bella’s budget increases to $20. Derive her new demand curve for bananas. Are bananas a normal or inferior good for Bella? Explain. 
4.  Suppose that there are two goods, X and Y. The utility function is U = X^{0.5}Y. The price of X is P, and the price of Y is $4. Income is $120. Derive the demand for X as a function of P. 
5.  Suppose that there are two goods, X and Y. The utility function is U = X^{2}Y^{2}. The price of X is P, and the price of Y is $50. Income is $600. Derive the demand for X as a function of P. 
6.  Suppose that there are two goods, X and Y. The utility function is U = XY + 2Y. The price of X is P, and the price of Y is $5. Income is $60. Derive the demand for X as a function of P. 
7.  Suppose that there are two goods, X and Y. The utility function is U = XY + 2Y. The price of X is $5, and the price of Y is P. Income is $60. Derive the demand for Y as a function of P. 
8.  To use calculus to decompose the total effect of a price change into substitution and income effects, it is necessary to solve all of the following EXCEPT the consumer’s:  
A)  utilitymaximization problem at the original prices.  
B)  utilitymaximization problem at the new prices.  
C)  expenditureminimization problem at the new prices and original utility level.  
D)  expenditureminimization problem at the original prices and new utility level. 
9.  For the Cobb–Douglas utility function:  
A)  the income and substitution effects are necessarily the same size.  
B)  the demand for each good is independent of changes in the price of the other good.  
C)  there is only an income effect, no substitution effect.  
D)  there is only a substitution effect, no income effect. 
10.  The size and direction of the income effect depend on all of the following EXCEPT:  
A)  the amount of the good (X) the consumer buys.  
B)  the change in the quantity of X when purchasing power is transformed (¶X(P_{X}, P_{Y},I)/¶I).  
C)  the change in the consumption of X as the price of X changes, holding utility constant.  
D)  whether the good is normal or inferior. 
11.  The Slutsky equation can be expressed as:  
A)  .  
B)  .  
C)  .  
D)  . 
12.  Which of the following statements about Marshallian demand curves is FALSE?  
A)  They show the relationship between price and quantity demanded, assuming that the consumer’s income stays constant.  
B)  They have an income effect as well as a substitution effect.  
C)  They have just a substitution effect.  
D)  They have the property that purchasing power changes when the good’s price changes. 
13.  Which of the following statements about Hicksian demand curves is FALSE?  
A)  They are also known as compensated demand curves.  
B)  They can be derived by solving the consumer’s expenditure minimization problem to find the bundle of goods after the price change that would give her the same level of utility as before the price change.  
C)  They indicate that the quantity demanded of X is inversely related to the price of X, all else equal.  
D)  They have an income effect as well as a substitution effect. 
14.  For the special case of a Giffen good, the partial derivative of quantity demanded with respect to price is _____, and the partial derivative of quantity demanded with respect to income is _____.  
A)  positive; positive  
B)  positive; negative  
C)  negative; positive  
D)  negative; negative 
15.  Which of the following statements about a Giffen good is FALSE?  
A)  It is very rare.  
B)  Its demand curve slopes upward.  
C)  The consumer buys a lot of an inferior good, and consumption of the good is very responsive to changes in income.  
D)  The substitution effect dominates the income effect. 
16.  Joaquin consumes pizza and beer. His utility function is
where P is the number of pizzas and B is glasses of beer. Joaquin has $30, and he plans to spend all of it on pizza and beer today. a. The price of one pizza is $10 and the price of beer is $3 per glass. Solve for Joaquin’s optimal bundle. b. Suppose that during happy hour Joaquin can get beer for $2. Find the substitution effect, the income effect, and the total effect of the decrease in the price. c. Are pizza and beer normal or inferior goods for Joaquin? Explain. 
17.  Suppose that a consumer has utility U(X,Y) = 2XY + X and income of $499 to spend on goods X and Y.
a. The prices of X and Y are $1 and $2 per unit respectively. Use a Lagrangian to solve for the optimal basket of goods. b. Suppose that the price of X increases to $2 per unit. Use a Lagrangian to solve for the new optimal basket of goods. Find the total effect of the price change on the consumption of each good. c. Use a Lagrangian to find the substitution effect of the increase in the price of good X on the consumption of each good. What income would the consumer need to attain the original level of utility if the price of X increased to $2 per unit? d. Find the income effect of the increase in the price of good X on the consumption of each good. Are the goods normal or inferior? Explain. e. Show that the total effect of the increase in the price of X is equal to the sum of the substitution effect and the income effect. 
18.  Suppose that Bella’s utility function from bananas (B) and chocolate (C) is
Her utility is 4, and the price of chocolate is $3. Derive Bella’s Hicksian demand for bananas. 
19.  Suppose that there are two goods, X and Y. The utility function is The price of Y is $1 per unit and the price of X is P. Derive the Hicksian demand curve for X for utility equal to 50,000 units. 
20.  Suppose that there are two goods, X and Y. The utility function is The price of Y is $2 per unit and the price of X is P. Derive the Hicksian demand curve for X for utility equal to 2,000 units. 
Answer Key
1.  B 
2.  C 
3.  a. To get Bella’s demand for burgers, solve her constrained optimization problem:
where p is the price of bananas. Let’s apply the utilitymaximization condition: Solve for C as a function of B and p: Plug this expression for C into the budget constraint and solve for B: is the demand for chocolate. b. Bella’s demand for bananas will change when her income increases from $15 to $20. Her constrained optimization problem will be The change in her income changes only her constraint. Therefore, the utilitymaximization condition and the relationship between C, B, and the price of bananas does not change. We can just plug this relationship into the new budget constraint and solve for B: is her new demand. Notice that Bella wants to consume more bananas at every price after her income increases. Therefore, bananas are a normal good for Bella. 
4.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l:
Solve for Y as a function of X and P:
Substitute this expression for Y in the last FOC:
Solve for X as a function of P to get the equation for the demand curve: 
5.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l: Solve for Y as a function of X and P:
Substitute this expression for Y in the last FOC:
Solve for X as a function of P to get the equation for the demand curve: 
6.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l: Solve for Y as a function of X and P:
Substitute this expression for Y in the last FOC:
Solve for X as a function of P to get the equation for the demand curve: 
7.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l: Solve for X as a function of Y and P:
Substitute this expression for X in the last FOC:
Solve for X as a function of P to get the equation for the demand curve: 
8.  D 
9.  B 
10.  C 
11.  D 
12.  C 
13.  D 
14.  B 
15.  D 
16.  a. Joaquin’s problem can be expressed as
or FOC: Solve for P as a function of B using the first two constraints: Plug into the budget constraint and solve for P* and B*: b. To find the substitution effect, solve Joaquin’s expenditure minimization problem using the lower price of beer with his original utility as the constraint. Joaquin’s original utility is: So his expenditure minimization problem is: or as a Lagrangian: FOC: Solve for P(B) using the first two conditions: Plug into the utility constraint and solve: Therefore, the substitution effect of the decrease in the price of beer is to consume 1.12 more beers (6.12 – 5) and 0.28 fewer pizzas (1.22 – 1.5). To get the income effect, we need to find the optimal bundle at the new price of beer and the original income. Joaquin’s problem now can be expressed as or FOC: Solve for P as a function of B using the first two constraints: Plug into the budget constraint and solve for P* and B*: So the income effect of the decrease in the price of beer is to consume 1.38 more beers (7.5 – 6.12) and 0.28 more pizzas (1.5 – 1.22). The total effect is to consume 2.5 more beers and the same number of pizzas. c. Because the income effect for both goods is positive (i.e., the quantity of each good increases as purchase power increases), both are both normal goods. 
17.  a. Write out the constrained utility maximization problem and the Lagrangian:
Take the firstorder conditions: Use the first two conditions to solve for Y(X): Plug into the budget constraint and solve for X* and Y*: b. Write out the constrained utility maximization problem and the Lagrangian: Take the firstorder conditions: Use the first two conditions to solve for Y(X): Plug into the budget constraint and solve for X* and Y*: Therefore, the total effect is: For X: For Y: c. First, calculate the utility at the optimal quantities from part a: Write out the expenditure minimization problem with the original utility as the constraint and the associated Lagrangian: Take the firstorder conditions of the Lagrangian: Use the first 2 two conditions to solve for Y(X): Plug into the utility constraint and solve for X* and Y*: Therefore, the substitution effect is: For X: For Y: As expected, the substitution effect indicates that the consumer wants to purchase fewer units of the more expensive good (X) and more units of the less expensive good (Y), holding utility constant. Finally, the consumer would need to spend to maintain the original level of utility after the price increase. d. The income effect is the difference between the final bundle after the price change and the bundle that the consumer would choose if prices increased but utility stayed the same as before the price increase: For X: For Y: The income effect indicates that the consumer chooses to buy fewer units of each good as purchasing power decreases, all else equal. Therefore, both X and Y are normal goods. e. For X, the substitution effect is –73.22 and the income effect is –51.78. The sum of these two effects is –125, which is the total effect of the price change on the consumption of X. Similarly for Y, the substitution effect is 51.78 and the income effect is –51.78. The sum of these two effects is zero, which is the total effect of the change in the price of X on the consumption of Y. 
18.  To get Bella’s Hicksian demand for bananas, solve her constrained optimization problem:
where p is the price of bananas. Let’s apply the utilitymaximization condition: Solve for C as a function of B and p: Plug this expression for C into the utility constraint and solve for B: The quantity of bananas demanded is inversely related to the price of bananas in the Hicksian demand. 
19.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l: Solve for Y as a function of X and P:
Substitute this expression for Y in the last FOC: Solve for X as a function of P to get the Hicksian demand: 
20.  Write out the constrained optimization problem and the Lagrangian:
The Lagrangian is: FOC: Solve the first two FOCs for l: Solve for Y as a function of X and P:
Substitute this expression for Y in the last FOC: Solve for X as a function of P to get the Hicksian demand: 
Use the following to answer question 1:
Figure 5.1
1.  (Figure 5.1) Francis spends his income on fishing charters and jumping out of airplanes. Which of the following statements is TRUE?  
A)  Fishing charters are an inferior good.  
B)  An increase in income could cause the optimal consumption bundle to move from point A to point B.  
C)  Parachute jumps are an inferior good.  
D)  An increase in the price of parachute jumps could cause the optimal consumption bundle to move from point A to point B. 
Use the following to answer question 2:
Figure 5.2
2.  (Figure 5.2) Hamburger meat is a(n) _____ good and canned tuna is a(n) _____ good.  
A)  normal; normal  
B)  inferior; normal  
C)  inferior; inferior  
D)  normal; inferior 
3.  When Logan earned $1,000 per week, he purchased 5 karate lessons and 40 gallons of gasoline. When his earnings increased to $1,100 per week, he purchased 6 karate lessons and 43 gallons of gasoline. The income elasticity of karate lessons and gasoline are _____ and _____, respectively.  
A)  0.50; 1.33  
B)  0.10; 1.6  
C)  2.00; 0.75  
D)  0.85; 0.15 
4.  Suppose that Seth’s income increases from $400 to $500 per week, so Seth increases his purchases of movies from 3 to 4. The income elasticity of movies is:  
A)  1.33.  
B)  0.25.  
C)  0.75.  
D)  1.00. 
Use the following to answer questions 56:
Figure 5.3
5.  (Figure 5.3) The curve that goes through the points A, B, C, and D is called the:  
A)  income elasticity curve.  
B)  optimal consumption path.  
C)  Engel curve.  
D)  income expansion path. 
6.  (Figure 5.3) Which of the following statements is TRUE?  
A)  Books are an inferior good at income levels greater than those associated with bundle B.  
B)  Books are an inferior good at income levels greater than those associated with bundle C.  
C)  Both books and paintings are normal goods up to the income level corresponding to bundle D.  
D)  Paintings are an inferior good at income levels higher than those associated with these bundles. 
7.  Ryan’s Engel curve for potato chips is I = 300C, where I is weekly income and C measures the number of bags of potato chips. Ryan considers potato chips a(n):  
A)  inferior good.  
B)  normal good.  
C)  inferior good at income levels above $60,000.  
D)  inferior good at income levels above $30,000. 
Use the following to answer question 8:
Figure 5.4
8.  (Figure 5.4) Which of the following statements is TRUE?  
A)  Fruitcake is an inferior good regardless of income level.  
B)  Fruitcake is a normal good regardless of income level.  
C)  Fruitcake is a normal good until income reaches $120, and then it becomes an inferior good.  
D)  Fruitcake is an inferior good until income reaches $120, and then it becomes a normal good. 
9.  Julie spends all of her income on gasoline and pizza. Gasoline costs $4 per gallon and pizza costs $2 per slice. When Julie’s income is $50 per week, she purchases 5 gallons of gasoline and 15 slices of pizza. When her income rises to $80 per week, she buys 15 gallons of gasoline and 10 slices of pizza. Which of the following statements is true?  
A)  Both gasoline and pizza are normal goods.  
B)  Gasoline is a luxury good.  
C)  Pizza is a luxury good.  
D)  Both gasoline and pizza are inferior goods. 
Use the following to answer question 10:
Figure 5.5
10.  (Figure 5.5) Suppose the consumer has $10 to spend on energy drinks and coffee. Which of the following figures represents the consumer’s demand curve for energy drinks?


A)  panel (a)  
B)  panel (b)  
C)  panel (c)  
D)  panel (d) 
Use the following to answer question 11:
Figure 5.6
11.  (Figure 5.6) Garth spends his income on ice cream and coffee, and coffee sells for $1 a cup. If ice cream sells for $1.50 per gallon, Garth will purchase:  
A)  2 gallons.  
B)  8 gallons.  
C)  1 gallon.  
D)  6 gallons. 
Use the following to answer question 12:
Figure 5.7
12.  (Figure 5.7) Based on the consumer’s indifference curves and budget constraints, which of the following demand curves reflects the consumer’s demand for water park tickets? Assume the consumer has income of $100.


A)  Demand curve A  
B)  Demand curve B  
C)  Demand curve C  
D)  Demand curve D 
Use the following to answer question 13:
Figure 5.8
13.  (Figure 5.8) Refer to Figure 5.8, depicting the consumer’s indifference curves and budget constraints. Suppose the consumer has $20 of income to spend on apple and prune juice. Which of the following statement(s) is (are) TRUE?


A)  I and II  
B)  II and III  
C)  II and IV  
D)  I 
14.  What is the substitution effect of a price change?  
A)  Consumers will buy more of the good whose relative price has risen and less of the good whose relative price has fallen.  
B)  When prices fall, consumers will have more purchasing power and buy more of the good whose price has fallen.  
C)  When prices fall, consumers will have more purchasing power and buy more of all goods.  
D)  Consumers will consume less of the good whose relative price has risen and more of the good whose relative price has fallen. 
15.  The income effect of a price change predicts that a _____ in a good’s price will _____ consumer purchasing power, leading to a(n) _____ in consumption of _____ goods.  
A)  fall; increase; increase; normal  
B)  fall; decrease; decrease; normal  
C)  rise; increase; increase; inferior  
D)  rise; increase; decrease; inferior 
Use the following to answer question 16:
Figure 5.9
16.  (Figure 5.9) When the price of milk drops, the substitution effect _____ the quantity of milk consumed from _____.  
A)  increases; 2 to 6 gallons  
B)  increases; 4 to 6 gallons  
C)  decreases; 6 to 2 gallons  
D)  increases; 2 to 4 gallons 
Use the following to answer question 17:
Figure 5.10
17.  (Figure 5.10) When the price of milk drops, the income effect _____ the quantity of milk consumed from _____.  
A)  increases; 2 to 6 gallons  
B)  increases; 4 to 6 gallons  
C)  decreases; 6 to 2 gallons  
D)  increases; 2 to 4 gallons 
Use the following to answer questions 1819:
Figure 5.11
18.  (Figure 5.11) When the price of football tickets increases, the substitution effect decreases the number of tickets bought from:  
A)  4 to 3.  
B)  6 to 3.  
C)  6 to 4.  
D)  20 to 8. 
19.  (Figure 5.11) When the price of football tickets increases, the income effect decreases the number of tickets bought from:  
A)  4 to 3.  
B)  6 to 3.  
C)  6 to 4.  
D)  20 to 8. 
Use the following to answer question 20:
Figure 5.12
20.  (Figure 5.12) The substitution effect will be largest for indifference curve:  
A)  U_{1}.  
B)  U_{2}.  
C)  U_{3}.  
D)  U_{4}. 
21.  In 2010, the average household spent $1,178 on telephone services and $333 on nonalcoholic drinks. From this information, we can conclude that:  
A)  the substitution effect of a price change will be larger for telephone services than for nonalcoholic drinks.  
B)  an increase in the price of telephone services will cause a larger income effect than a similar increase in the price of nonalcoholic drinks.  
C)  an increase in the price of nonalcoholic drinks will cause a larger income effect than a similar increase in the price of telephone services.  
D)  the substitution effect of a price change will be larger for nonalcoholic drinks than for telephone services. 
22.  Which of the following statements are TRUE?


A)  I, II, and IV  
B)  I and IV  
C)  II and III  
D)  III and IV 
Use the following to answer question 23:
Figure 5.13
23.  (Figure 5.13) Which of the following statements is (are) TRUE?


A)  I and II  
B)  II and III  
C)  III and IV  
D)  I 
Use the following to answer questions 2425:
Figure 5.14
24.  (Figure 5.14) Because of the income effect associated with the decrease in the price of good X, the quantity of good X purchased:  
A)  increases from 3 to 4.  
B)  increases from 4 to 5.  
C)  decreases from 5 to 4.  
D)  increases from 3 to 5. 
25.  (Figure 5.14) Good X is a(n) _____ good, and good Y is a(n) _____ good.  
A)  normal; inferior  
B)  normal; normal  
C)  inferior; inferior  
D)  inferior; normal 
Use the following to answer questions 2628:
Figure 5.15
26.  (Figure 5.15) Because of the substitution effect associated with the decrease in the price of good X, the quantity of good X purchased:  
A)  increases from 3 to 5.  
B)  decreases from 3 to 2.  
C)  increases from 2 to 3.  
D)  increases from 2 to 5. 
27.  (Figure 5.15) Because of the income effect associated with the decrease in the price of good X, the quantity of good X purchased:  
A)  increases from 3 to 5.  
B)  decreases from 5 to 2.  
C)  decreases from 3 to 2.  
D)  decreases from 5 to 3. 
28.  (Figure 5.15) What type of good is good X?


A)  I and III  
B)  III  
C)  II and III  
D)  I 
Use the following to answer questions 2930:
Figure 5.16
29.  (Figure 5.16) The substitution effect of the price increase causes consumption of baseball hats to:  
A)  decrease by 1.  
B)  decrease by 3.  
C)  decrease by 4.  
D)  increase by 1. 
30.  (Figure 5.16) The income effect of the price increase causes consumption of baseball hats to:  
A)  decrease by 1.  
B)  decrease by 3.  
C)  decrease by 4.  
D)  increase by 1. 
31.  A consumer’s bundle includes two normal goods, X and Y. According to the income effect, a(n) _____ in the price of good X or a(n) _____ in the price of good Y will cause the consumer to buy less of good X.  
A)  increase; decrease  
B)  increase; increase  
C)  decrease; increase  
D)  decrease; decrease 
32.  A consumer’s bundle includes the inferior good X and the normal good Y. According to the income effect, a(n) _____ in the price of good X or a(n) _____ in the price of good Y will cause the consumer to buy more of good X.  
A)  increase; decrease  
B)  increase; increase  
C)  decrease; increase  
D)  decrease; decrease 
33.  The substitution effect of a price increase:  
A)  causes the consumer to purchase less of the good that is now relatively more expensive.  
B)  causes the consumer to purchase more of the good whose price has risen.  
C)  can cause the consumer to purchase either more or less of the good.  
D)  has no effect on the amount purchased of either good. 
34.  For Sara, ramen noodles are a normal good, however Sean considers ramen noodles to be inferior. If Sara and Sean have the same amount of income:  
A)  Sean’s income effect will be stronger than Sara’s income effect.  
B)  Sean’s substitution effect will be stronger than Sara’s substitution effect.  
C)  Sean’s demand for ramen noodles will be more price elastic than Sara’s.  
D)  Sean’s demand for ramen noodles will be less price elastic than Sara’s. 
Use the following to answer question 35:
Figure 5.17
35.  (Figure 5.17) Given the change in the budget constraint, which of the following statements is TRUE?  
A)  The demand curve for good Y shifted inward.  
B)  The demand curve for good X shifted outward.  
C)  Good X is an inferior good.  
D)  Good X and good Y are complements. 
Use the following to answer questions 3637:
Figure 5.18
36.  (Figure 5.18) Good X and good Y are:  
A)  perfect complements.  
B)  Giffen goods.  
C)  complement goods.  
D)  substitute goods. 
37.  (Figure 5.18) Which of the following statements are TRUE?


A)  II and III  
B)  I, III, and IV  
C)  III and IV  
D)  I and IV 
38.  Suppose the price of good X, a Giffen good, increases. Which of the following statements are TRUE?


A)  I and IV  
B)  II and IV  
C)  I and III  
D)  II and III 
Use the following to answer questions 3940:
Figure 5.19
39.  (Figure 5.19) The price of good Y _____, increasing the consumption of both good Y and good X, which are _____.  
A)  increased; complements  
B)  decreased; substitutes  
C)  increased; substitutes  
D)  decreased; complements 
40.  (Figure 5.19) Given the change in the budget constraint, the demand curve for _____ shifted _____.  
A)  good X; inward  
B)  good Y; outward  
C)  good X; outward  
D)  both good X and good Y; outward 
Use the following to answer question 41:
Figure 5.20
41.  (Figure 5.20) The crossprice elasticity of demand for good X with respect to good Y is _____ in panel (a) and _____ in panel (b).  
A)  zero; negative  
B)  negative; positive  
C)  positive; negative  
D)  negative infinity; positive 
42.  Suppose that good X and good Y are substitutes and good X and good Z are complements. When the price of a good Y _____ or the price of good Z _____, the demand for good X shifts outward.  
A)  increases; decreases  
B)  increases; increases  
C)  decreases; decreases  
D)  decreases; increases 
43.  Suppose the demand for good X shifts in. Which of the following statements is (are) TRUE?


A)  I, II, and III  
B)  II and III  
C)  I  
D)  II 
44.  Which of the following statements is TRUE?


A)  I only  
B)  II only  
C)  I, II, and III  
D)  I and II 
45.  To calculate the market demand curve from individual demand curves:  
A)  vertically sum the individual demand curves.  
B)  horizontally sum the individual demand curves.  
C)  exponentiate the individual demand curves.  
D)  add up the prices of the individual demand curves, holding the quantities constant. 
Use the following to answer question 46:
Figure 5.21
46.  (Figure 5.21) Suppose Milli and Vanilli are the only two customers in the market for voice lessons. Milli’s demand is Q_{M} = 40 – 4P, and Vanilli’s demand is Q_{V} = 75 – 5P. Which panel represents the market demand for vocal lessons?  
A)  panel (a)  
B)  panel (b)  
C)  panel (c)  
D)  panel (d) 
47.  There are 10 consumers in the market, each with the following demand curve: Q = 100 – 0.5P. In a graph of the market demand curve, its slope (DP/DQ) would equal:  
A)  –0.50.  
B)  –0.20.  
C)  –1.50.  
D)  –2.25. 
48.  There are only three consumers in the market, and their demand equations are as follows: (1) Q = 5 – 0.5P, (2) Q = 10 – P, and (3) Q = 2 – 0.2P. What is the equation for the market demand curve?  
A)  P = 30 – 8Q  
B)  Q = 3.75 – 0.125P  
C)  Q = 17 – 1.7P  
D)  Q = 30 – 2P 
49.  Suppose the market for a good is composed of 1,000 identical consumers. The market’s demand curve is given by Q_{M} = 150,000 – 25P. What is the equation for an individual consumer’s demand curve?  
A)  Q = 150,000,000 – 25,000P  
B)  Q = 6,000,000 – 40P  
C)  Q = 6 – 4P  
D)  Q = 150 – 0.025 
Use the following to answer question 50:
Figure 5.22
50.  (Figure 5.22) Suppose there are only two consumers in the market for good X. The total quantity demanded in the market at a price of $3 is _____, and the total quantity demanded in the market at a price of $12 is _____.  
A)  20; 2  
B)  20; 5  
C)  6; 3  
D)  18; 0 
51.  The market for good X consists of only two consumers; their demand curves are given by Q = 10 – 0.10P and Q = 5 – 0.10P. What is the market demand curve?  
A)  Q_{M} = 15 – 0.2P if P ³ $50, and Q_{M} = 5 – 0.10P if P < $50  
B)  Q_{M} = 15 – 0.2P if P ³ $50, and Q_{M} = 10 – 0.10P if P < $50  
C)  Q_{M} = 15 – 0.2P if P < $50, and Q_{M} = 10 – 0.10P if P > $50  
D)  Q_{M} = 15 – 0.2P 
52.  Sally is one of many consumers in the yellow onion market. Which of the following statements is (are) TRUE?


A)  II and III  
B)  I  
C)  II  
D)  III 
53.  There are 100 consumers in the market for good X, each with a demand curve given by Q = 2/P. What is the market demand curve for good X?  
A)  Q_{M} = 0.5P  
B)  Q_{M} = 200 – 200P  
C)  Q_{M} = 1/50P  
D)  Q_{M} = 200/P 
54.  The market for macaroni and cheese has only two consumers, David and Wallace. Market demand for macaroni and cheese will tend to be more elastic if:  
A)  David and Wallace consider macaroni and cheese to be a necessity good rather than a luxury good.  
B)  David and Wallace consider macaroni and cheese to be an inferior good rather than a normal good.  
C)  David and Wallace consider macaroni and cheese to be a normal good rather than an inferior good.  
D)  David and Wallace consider macaroni and cheese to be an economic “bad.” 
55.  Eugene has $100 to spend on video blackjack at $1 per game and French fries at $1 per basket.

56.  Blaze has $200 to spend on fishing equipment and fastfood burgers. Fishing equipment is priced at $10 per unit and fastfood burgers are priced at $4 per burger.

Use the following to answer question 57:
Figure 5.23
57.  (Figure 5.23) In panel (a), the price of good X is $1.50 per unit and the price of good Y is $3 per unit. In panel (b), the consumer’s income increased from $400 to $480.

Use the following to answer question 58:
Figure 5.24
58.  (Figure 5.24) Answer the following questions:

Use the following to answer question 59:
Figure 5.25
59.  (Figure 5.25) Answer the following questions:

60.  Alec has $40 weekly to spend on restaurant meals (priced at $10 per meal) and bowling (priced at $2 per game).

Use the following to answer question 61:
Figure 5.26
61.  (Figure 5.26) This graph shows the demand curve for skirts. Suppose the consumer has $500 to spend on skirts and handbags, and the price of handbags remains unchanged at $100. Using budget constraints and indifference curves, placing skirts on the horizontal axis and handbags on the vertical axis, illustrate two of the consumer’s optimal consumption bundles of skirts and handbags. 
62.  Bob’s utility function for black (B) and white (W) socks is U = 10B + 10W, where MU_{B} = 10 and MU_{W} = 10. Suppose that Bob has $40 to spend on socks. With the price of white socks held constant at $10, graph Bob’s demand curve for black socks at $2, $4, $5, $8, $10, and $20. 
63.  For the following scenarios, explain the direction of the substitution effect, income effect, and total effect.

Use the following to answer question 64:
Figure 5.27
64.  (Figure 5.27) Illustrate the substitution effect and income effect associated with the decrease in the price of milk. Label the substitution effect A to A¢ and the income effect A¢ to B. 
Use the following to answer question 65:
Figure 5.28
65.  (Figure 5.28) Answer the following questions.

66.  Suppose a consumer spends her income on lobster and frozen pizza. Assume that the consumer has an income of $60, the price of lobster is $6, and the price of frozen pizza is $6.

67.  A consumer’s bundle includes good X and good Y. Determine whether the following statements are true, false, or uncertain.

Use the following to answer question 68:
Figure 5.29
68.  (Figure 5.29) The price of good Y decreased from $20 to $10.

69.  Suppose a consumer spends $100 of income on two goods: buying 4 units of good X (priced at $10) and 3 units of good Y (priced at $20). Both are substitute goods. Using indifference curves and budget constraints, illustrate the effect of a $10 decrease in the price of good Y on the consumer’s optimal consumption bundle. 
Use the following to answer question 70:
Figure 5.30
70.  (Figure 5.30) The price of good Y increased from $1.00 to $5.00.

Use the following to answer question 71:
Figure 5.31
71.  (Figure 5.31) Assume that Roscoe and Roland comprise the entire market of buyers.

Use the following to answer question 72:
Figure 5.32
72.  (Figure 5.32) Graph the market demand curve for bumper stickers, assuming that Neal and Vince are the only two consumers in the market for bumper stickers. On your graph, show the quantity demanded at $10, $7.50, $5, $2.50, and $0. 
73.  Ricki, CC, and Brett are the only consumers in the market for leather jackets; their inverse demand curves, respectively, are as follows:
P = 200 – 10Q_{R} P = 200 – 50Q_{CC} P = 200 – 20Q_{B} What is the equation for the market demand curve for leather jackets? 
74.  Suppose there are 100 consumers in the computer speaker market, each with an identical demand curve given by Q_{i} = 10 – 0.1P, where P is the price per pair of speakers and Q_{i }measures the quantity demanded of computer speakers by each person. The market supply for computer speakers is given by Q^{S} = 20P – 200. What are the equilibrium price and quantity in the computer speaker market? 
75.  The utility function for a consumer is U = min{0.25X, Y}. What is the equation for the consumer’s income expansion path? 
76.  A consumer has the following utility function: U = 4X + 2Y, where X is the number of slices of plain pizza and Y is the number of slices of pepperoni pizza. Given this person’s preferences, what is the demand curve for slices of plain pizza? 
Use the following to answer question 77:
Figure 5.33
77.  (Figure 5.33) The consumer has an income of $15 and the utility function U = 5X + 5Y. Before the price change the consumer will consume _____units of Y and _____units of X. After the change, she will consume _____units of Y and _____units of X. 
Use the following to answer question 78:
Figure 5.34
78.  (Figure 5.34) For an income of $15, the price of Y falls by _____, leading to a substitution effect of _____and an income effect of _____ . 
Use the following to answer question 79:
Figure 5.35
79.  For a constant income, the crossprice elasticity of demand between good X and Y in figure A is _____. In figure B it is _____ 
80.  Abby’s utility function is given by U = X^{2}Y^{2}. For this utility function, MU_{x }= 2XY^{2} and MU_{y }= 2X^{2}Y. If good X costs $10 and good Y costs $5, what share of Abby’s utilitymaximizing bundle is made up of good X? 
Use the following to answer question 81:
Figure 5.36
81.  (Figure 5.36) The figure shows two budget lines for a consumer whose preferences are represented by the utility function U = 2G + F, where G represents the number of video games and F represents the number of baskets of fries. What is the demand equation for this consumer? 
Use the following to answer question 82:
Figure 5.37
82.  (Figure 5.37) What is the demand equation? 
Use the following to answer question 83:
Figure 5.38
83.  (Figure 5.38) Cameron, Gillian, Bob, and Peter are the only consumers in the market for kayaks; their inverse demand curves, respectively, are as follows:
P = 5,000 – 1,000Q_{C} P = 4,000 – 1,000Q_{G} P = 3,000 – 500Q_{B} P = 3,000 – 1,500Q_{P} _{ } What is the market demand curve for kayaks based on these four individuals? 
Answer Key
1.  B  
2.  B  
3.  C  
4.  A  
5.  D  
6.  C  
7.  B  
8.  C  
9.  B  
10.  B  
11.  A  
12.  A  
13.  B  
14.  D  
15.  A  
16.  D  
17.  B  
18.  C  
19.  A  
20.  A  
21.  B  
22.  D  
23.  A  
24.  C  
25.  D  
26.  A  
27.  B  
28.  C  
29.  A  
30.  B  
31.  B  
32.  B  
33.  A  
34.  D  
35.  B  
36.  D  
37.  C  
38.  C  
39.  D  
40.  C  
41.  B  
42.  A  
43.  B  
44.  D  
45.  B  
46.  B  
47.  B  
48.  C  
49.  D  
50.  A  
51.  C  
52.  D  
53.  D  
54.  C  
55. 
(Note: The location of point B and indifference curve U_{2} will vary in students’ answers.) 

56. 


57. 


58.  a. The income expansion path is a curve that shows the utilitymaximizing consumption bundles for different levels of income.
b. 2, 5, 7, and 8 c.


59.  a. The price of good X decreased, falling from $20 ($40/2) to $10 ($40/4).
b.


60.  a. and b.
c. 

61.  
62.  Bob will purchase the color sock that gives him the most marginal utility per dollar (MU/P). Once the price of black socks rises above $10, the marginal utility per dollar of black socks will be less than the marginal utility per dollar of white socks, and Bob will buy only white socks.
When black socks cost $10, their marginal utility per dollar (10/10 = 1) equals the marginal utility per dollar of white socks (10/10 = 1). In this case, Bob is indifferent between white socks and black socks because each item gives the same marginal utility per dollar. If Bob decides to spend all his money on black socks, he can purchase 4 pairs (40/10). If, however, Bob spends his entire $40 on 4 pairs of white socks, he has no money to buy black socks. This explains why the demand curve for black socks is horizontal between 0 and 4 pairs when the price of black socks is $10.


63.  In the first scenario, the substitution effect causes the consumer to purchase fewer units of good X. The income effect of the price increase also causes the consumer to purchase fewer units of good X. The total effect is that consumption of good X decreases.
In the second scenario, the substitution effect leads the consumer to buy more units of good X, while the income effect causes the consumer to buy fewer units of good X. The total effect is that the consumption of good X increases, given that the substitution effect dominates the income effect. (Note: If the income effect dominated the substitution effect, X would be a Giffen good.)
In the third scenario, the substitution effect leads to decreased consumption of good X. The income effect causes the consumer to buy more units of good X. For a Giffen good, the income effect outweighs the substitution effect, and the consumption of good X increases. 

64. 
The substitution effect is given by the move from point A to point A¢, and the income effect is given by the move from point A¢ to point B. 

65.  a. The income effect reflects the movement from A¢ to B, or a 3unit decrease in consumption of scallops. The substitution effect reflects the movement from A to A¢, or a 1unit decrease in the consumption of scallops.
b. Scallops are a normal good because a decrease in purchasing power caused the consumer to buy fewer scallops. c. Beef jerky is an inferior good because the decrease in purchasing power caused the consumer to buy more beef jerky. 

66.  a.
For an inferior good, the income effect of a price decrease is negative and is dominated by the positive effect of the substitution effect.
b.
For a Giffen good, the income effect of a price decrease is negative and dominates the positive effect of the substitution effect. 

67.  a. False. The substitution effect leads the consumer to buy less of good X, and the income effect leads the consumer to buy less of good X because it is a normal good.
b. True. The substitution effect leads the consumer to buy less of good X, but the income effect leads the consumer to buy more of good X because it is an inferior good. Overall, the substitution effect dominates the income effect. c. True. The substitution effect leads the consumer to buy more of good X, but the income effect leads the consumer to buy less of it. With a Giffen good the income effect dominates the substitution effect. 

68.  a. Goods X and Y are complements: the fall in the price of good Y leads to an increase in the quantity purchased of good X.
b. The price of good Y decreased by 50% and the quantity purchased of good X increased by 25%. The crossprice elasticity is 25/–50 = –0.5. 

69.  
70.  a. Goods X and Y are substitutes because the rise in the price of good Y led to an increase in the quantity purchased of good X.
b. The price of good Y increased by 400%, and the quantity purchased of good X increased by 150%. The crossprice elasticity is 150/400 = 0.375. c. The demand curve for good X shifted outward. 

71.  a.


72.  
73.  First, solve for each person’s demand curve:
Q_{R} = 20 – 0.1P, Q_{CC} = 4 – 0.02P, and Q_{B} = 10 – 0.05P. The market demand curve is Q = Q_{R} + Q_{CC} + Q_{B} = 34 – 0.17P. 

74.  The market demand curve = Q^{D} = 100 × Q_{i} = 100(10 – 0.1P) = 1,000 – 10P.
Set Q^{D} = Q^{S} and solve for P: 1,000 – 10P = 20P – 200 P = $40 Q = 600 

75.  The consumer’s utility function represents prefect complements in a 4:1 ratio. This implies that the consumer’s equilibrium will lie on a ray from the origin with equation Y = 1/4x.  
76.  The two types of pizza are perfect substitutes in a 2:1 ratio. In other words, to keep utility constant this consumer will trade 1 slice of plain pizza for 2 slices of pepperoni pizza. This implies that the consumer will be indifferent between the two types of pizza whenever the price ratio is equal to 2, will choose only pepperoni when the price ratio is above 2, and will choose only plain when it is below 2. The leads to the demand curve for plain pizza:
Q^{D}_{Plain} = 0 if P^{X}/P^{Y}>2 2x + U/2 if P^{X}/P^{Y} = 2 U/2 if P^{X}/P^{Y} < 2 

77.  BC_{1 }shows that the price of X is $1 ($15/15) and the price of Y is $1.80 ($15/8). For BC_{2 }the price of X remains at $1 and the price of Y falls to $1. This means that on BC_{1 }the price of Y is greater than the price of X, so the consumer will buy 15 units of X and 0 units of Y. Once the price of Y falls, making the prices equal, the consumer will be indifferent between any combination of X and Y that totals 15 units. (The indifference curve and budget line will be the same line.)  
78.  $0.80_80 cents  
79.  2.5; –1.67
Since income does not change and the amount of good Y doubles as a result of its price falling, we can conclude that the price has fallen by 50% in panel (a) but has risen by 100% in panel (b). The amount of good X rises by (9 – 4)/4 = 125%; in panel (b) it rises by 167%. Since cross elasticity is the percent change in the quantity of X due to a percent change in the price of Y, we can conclude that the crossprice elasticity of demand in panel (a) is 125/50 = 2.5, and in panel (b) it is –167/100 = –1.67. The products are complements in panel (a) but substitutes in panel (b). 

80.  The marginal rate of substitution (MRS) for Abby will be MU_{x/}MU_{y }= 2XY^{2/}2 X^{2}Y = Y/X. In equilibrium, MRS = the price ratio, or Y/X = 10/5 = 2, which implies that she will spend twice as much on Y as she does on X.  
81.  The consumer’s utility function represents perfect substitutes in a 2:1 ratio (1 basket of fries to 1 video game) for a marginal rate of substitution (MRS) of –0.5. The price ratio for both budget lines is P_{F/}P_{G} = –1. This implies that when the indifference curves are flatter than the budget lines, the result is a corner solution: this consumer purchases 150 video games for total utility of 300. If the price ratio were larger than the MRS, then the consumer would purchase only fries. If the price ratio equaled the MRS, the consumer would be indifferent between the two products. This leads to the following demand equation for video games:
If P_{F/}P_{G }> 0.5, then G = 0 If P_{F/}P_{G} < 0.5, then G = Income/P_{G} If P_{F/}P_{G} = 0.5, then G = Income/P_{G} – 0.5F 

82.  Note the kink at a price of $5 and a quantity of 2 units. This will lead to a twosegment demand curve with price ranges of $5 < P < $10 and P < $5. The segment above $5 will be Q = 4 – 0.4P and below $4 it will be Q = 14 – 2.4P.  
83.  To find the market demand curve, first find each inverse demand curve:
P = 5,000 – 1,000Q_{C}, or Q_{C} = 5 – 0.001P P = 4,000 – 1,000Q_{G}, or Q_{G} = 4 – 0.001P P = 3,000 – 500Q_{B}, or Q_{B} = 6 – 0.002P P = 3,000 – 1,500Q_{P}, or Q_{P} = 2 – 0.0007P
From the inverse demand curves we can see that Cameron has the highest demand choke price, followed by Gillian and then both Bob and Peter. If the price is in the $4,000 to $5,000 range, only Cameron will buy. From $3,000 to $4,000, both Gillian and Cameron will buy. Finally, when the price falls below $3,000, everyone will buy. This means that the demand equation for P > $4,000 is Q_{C} = 5 – 0.001P; for $4,000 < P < $5,000, it is Q = 9 – 0.002P; for $3,000 < P < $4,000 it is Q = 17 – 0.0047P. 
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