ADDITIONAL EXERCISEs FOR ASSIGNMENT
n Questions
n Checkpoint 13.1 ConsumptionPossibilities
1. Martha's cake and pasta budgetis $24 a week. The price of a cake is $4, and the price of a dish of pasta is$6.
1a. List the combinations of cake and pasta that are on Martha’s budgetline.
1b. Draw a graph of Martha's budget line with pasta plotted on the x-axis.
1c. If the price of a dish of pasta is halved, what is the change in therelative price of a cake? Explain your answer.
1d. Describe how Martha's budgetline in (b) changes if the following events occur one at a time and otherthings remain the same:
The price of a dish of pastafalls.
The price of a cake falls.
Martha's cake and pastabudget decreases.
2. The price of a bag of popcornis $2, the price of a can of soda is $1, and Bobby’s budget for popcorn andsoda is $10.
2a. List the affordable combinationsof cans of soda and bags of popcorn that are on Bobby’s budget line.
2b. What is the relative price of abag of popcorn?
2c. Suppose Bobby’s budgetincreases to $12 but the prices of a bag of popcorn and a can of soda do notchange. What happens to the relative price of a bag of popcorn?
n Checkpoint 13.2 MarginalUtility Theory
3. The table shows Wendy's total utility fromtacos and movies. The price of a taco is $2, the price of a movie is $8, andWendy has $22 a week to spend on tacos and movies.
3a. Calculate Wendy's marginalutility from the third movie in the week.
3b. Calculate the marginal utilityper dollar from movies when Wendy sees 3 movies a week.
3c. Calculate Wendy's marginalutility from the fourth taco in the week.
3d. Calculatethe marginal utility per dollar from tacos when Wendy buys 4 tacos a week.
3e. If Wendy sees 2 movies and buys2 tacos a week, is she maximizing total utility? Explain your answer. If Wendyis not maximizing total utility, explain how she would adjust her consumptionchoice to do so.
| Popcorn | Soda | ||
| Bags | Total | Cans | Total |
| 0 | 0 | 0 | 0 |
| 1 | 40 | 1 | 30 |
| 2 | 60 | 2 | 50 |
| 3 | 70 | 3 | 65 |
| 4 | 75 | 4 | 70 |
| 5 | 77 | 5 | 73 |
4. The table has Bobby’s totalutility from popcorn and soda. Assume the price of a bag of popcorn is $2, theprice of a can of soda is $1, and Bobby’s budget is $10. What is the Bobby’sutility maximizing combination of cans of soda and bags of popcorn ?
n Answers
n Checkpoint 13.1 ConsumptionPossibilities
1a. Thecombinations of cake and pasta that are on Martha’s budget line are:
0cake and 4 dishes of pastas
3cakes and 2 dishes of pastas
6cakes and 0 dishes of pasta
1b. Figure 12.1 shows Martha’sbudget line.
1c. The relative price of a cake is the number ofdishes of pasta that Martha must forgo to get 1 cake. The relative price of acake equals the price of a cake divided by the price of a dish of pasta. At theinitial prices, the relative price is $4 a cake ¸ $6 a dish of pasta, which is 2/3 of a dish of pasta per cake. Whenthe price of a dish of pasta falls to $3, the relative price of a cake is $4 acake ¸ $3 a dish ofpasta, which is 1 1/3 of a dish of pasta per cake. Then fall in the price of adish of pasta raises the relative price of a cake.
1d. If the price of a dish of pasta falls, thebudget line rotates outward and becomes flatter. The vertical intercept staysthe same, while the horizontal intercept increases.
If the price of a cake falls,the budget line rotates outward and becomes steeper. The horizontal interceptstays the same, while the vertical intercept increases.
If Martha’s budget decreases,the new budget line shifts inward and is parallel to the old budget line.
2a. The affordable combinations are 0 bags of popcorn and 10 cans ofsoda; 1 bag of popcorn and 8 cans of soda; 2 bags of popcorns and 6 cans ofsoda; 3 bags of popcorns and 4 cans of soda; 4 bags of popcorns and 2 cans ofsoda; and 5 bags of popcorns and 0 cans of soda.
2b. The relative price of a bag of popcorn is thenumber of cans of soda that Bobby must forgo to get 1 bag of popcorn. Therelative price of a bag of popcorn equals the price of a bag of popcorn dividedby the price of a can of soda, which is $2 a bag of popcorn ¸ $1 a can of soda = 2 cans of soda per bag of popcorn.
2c. Because neither the price of a bag of popcornnor a can of soda changes, the relative price of a bag of popcorn does notchange. A change in a person’s budget does not change relative prices.
n Checkpoint 13.2 MarginalUtility Theory
3a. The total utility of 3 movies is 84 units andthe total utility of the 2 movies is 60 units. The change in total utility,which equals the marginal utility, is (84 units) - (60 units equals 24 units.
3b. The marginal utility per dollar from movieswhen Wendy sees 3 movies is 24 ¸ $8 = 3units per dollar.
3c. The total utility of the 4 tacos is 30 unitsand the total utility of the 3 tacos is 27 units. The marginal utility of the4th taco equals (30 units) - (27units), which is 3 units.
3d. The marginal utility per dollar from the 4thtaco is 3 units ¸ $2 a taco,which is 1 1/2 units per dollar.
3e. Wendy is not maximizing her utility. She isnot allocating all of her budget because she is spending only $20. And the marginalutility per dollar from tacos is 4 1/2 units per dollar, which does not equalthe marginal utility per dollar from movies, which is 3 1/2 units per dollar.To maximize her utility, Wendy should buy 1 more taco. If she buys 1 more taco,she will consume 3 tacos and 2 movies. This combination allocates all of herincome and sets the marginal utility per dollar from tacos equal to that frommovies, with both equal to 3 1/2 units per dollar.
4. To maximize his utility, Bobby buys 4 cansof soda and 3 bags of popcorns. This combination allocates the entire budgetand equates the marginal utility per dollar from cans of soda and bags ofpopcorn, with each equal to 5 units per dollar.
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