ECN 221 Chapter 5 practice problems This is not due for a grade 1. Assume the price of pizza is $2.00 and the price of Beer is $1.00 and that at your current levels of consumption, the Marginal Utility from pizza is 10 and the Marginal Utility from beer is 6. True or false: You can increase total utility by buying more beer and less pizza. TRUE Calculate the marginal utility per dollar from each of the goods: Pizza: MU/$ = 10/2 = 5 Beer: MU/$ = 6/1 = 6 you receive higher marginal utility from a dollar spent on beer than from pizza, so to increase your total utility you should buy more beer and less pizza. 2. The price of steak is $7 per pound, and the price of chicken is $2 per pound. Your mother currently receives a marginal utility of 14 from consuming steak this week and 6 from consuming chicken this week. The marginal utility of chicken is therefore less than that of steak. Does this imply that your mother should buy less chicken this week? Explain. No. the marginal utility per dollar is 2 from steak and 3 from chicken, therefore mom can increase total utility by spending more money on chicken and less on steak. 3. Explain the equimarginal principle as it pertains to the consumption of two or more goods. Why is the resulting quantity of these goods referred to as a consumer equilibrium? The utility maximizing rule or the equimarginal principle is the rule to follow to find the utility maximizing combination of 2 or more goods. This combination is the one for which the marginal utility per dollar spent is as close to equal as possible across the goods (and for which all income is spent). If the marginal utility per dollar is higher for one good, total utility can be increased by buying more of that good and less of the other good. When the marginal utility per dollar is equal across goods, then we can no longer increase total U by moving dollars between goods we re doing the best we can given prices and income. A Consumer Equilibrium is attained when the utility-maximizing bundle of goods is purchased and all other things are held constant. In other words, by following the equimarginal principle, consumers reach an equilibrium, in that they will not change their consumption of the goods since they have found the combination that gives them the highest utility.
4. Consider the following data showing Bob s total utility from the consumption of two goods: Winston Cup Races and Broadway musicals. Assume the price of races is $50.00 (Bob gets his tickets early), the price of Broadway musicals is $100.00 (Bob likes to sit in the orchestra section), and Bob has $300 to spend on the two goods. Number of Races U MU MU/$ Number of Musicals U MU MU/$ 1 1,000 1000 20 1 1,000 1000 10 2 1,800 800 16 2 1,800 800 8 3 2,500 700 14 3 2,500 700 7 4 3,000 500 10 4 3,000 500 5 5 3,200 200 4 5 3,200 200 2 a. (6) Assuming that he wishes to maximize his utility, what combination of Winston Cup Races and Broadway musicals will Bob purchase? Carefully justify your answer. For each good you must calculate marginal utility (MU) and the marginal utility per dollar (MU /$). The marginal utility per dollar is found by dividing marginal utility by the price of the good. Now look to see where the equimarginal principle is satisfied. At 4 races and 1 musical, the marginal utility per dollar is equal across the goods, so this is the utility-maximizing combination. Note that this exactly uses up Bob s $300 income (4 races at $50 each = $200 and 1 musical at $100 each = $100). b. (3) If the price of musicals doubles, what will happen to Bob s consumption of the two goods? Explain. If the price of musicals doubles, the marginal utility per dollar is cut in half for each unit. The new values look like this: Number of Races U MU MU/$ Number of Musicals U MU MU/$ 1 1,000 1000 20 1 1,000 1000 5 2 1,800 800 16 2 1,800 800 4 3 2,500 700 14 3 2,500 700 3.5 4 3,000 500 10 4 3,000 500 2.5 5 3,200 200 4 5 3,200 200 1 Now we see that the equimarginal principle is satisfied at 5 races and 2 musicals, but Bob cannot afford this combination with available income and prices. So, in this case, he will purchase 5 races and 0 musicals and have $50 left over (he can buy a mark martin hat and tee shirt at the races). To see how this is found, simply spend the income one purchase at a time, and for each purchase, always buy the good that yields the highest marginal utility per dollar. 5. Assume that UB40 CD s are a normal good for you, and that you regularly purchase these CD s. Following is a decrease in the price of UB40 CD s: a. You will consume fewer CD s because there is no income effect. b. You will consume more CD s because both the income and substitution effect dictate that you do so. c. You will consume more CD s because both the income effect always outweighs the substitution effect for normal goods. d. Your consumption of CD s will not change because the substitution effect and income effect will offset each other. e. You can t be sure whether you will increase or decrease consumption of CD s without knowing the relative sizes of the income effect and substitution effect. B
6. Matt eats five slices of pizza on a Saturday night but admits each slice of pizza doesn't taste as good as the previous one. This suggests that for Matt a The marginal utility of a slice of pizza is positive but decreasing. b. The marginal utility of a slice of pizza is negative. c. The total utility of slices of pizza is declining. d. The total utility of slices of pizza is increasing by larger and larger increments. e. The law of diminishing marginal utility does not hold for Matt A 7. Fill in the missing information in the table below: UNITS TOTAL UTILITY MARGINAL UTILITY 0 0 ---- 1 100 a. 100 2 150 b. 50 3 175 c. 25 4 d. 190 15 8. Consider the following data describing how total benefits change with your consumption of SCUBA diving trips in Key Largo per year. Assume the price of each trip is $300.00 and this price accurately represents the marginal cost to you. Q (# trips) Price (MC) Total Benefits ($) marginal benefit 0-0 - 1 300 750 750 2 300 1250 500 3 300 1550 300 4 300 1700 150 5 300 1800 100 (a) How many trips will you take per year? Explain. calculate marginal benefits and find the point where MB = MC. Q* is 3 units. (b) What is the total consumer surplus from this number of trips? consumer surplus is total net benefits at Q* = $450 + $200 + $0 = $650
9. Consider the following data describing the change in Johnny s utility when he consume various levels of apples and grapefruit. The price of apples is $0.50, and the price of grapefruit is $1.00. Q apples TU Apples MU MU/$ Q Grapefruit TU Grapefruit MU MU/$ 0 0-0 0 0-0 1 10 10 20 1 25 25 25 2 18 8 16 2 40 15 15 3 25 7 14 3 53 13 13 4 30 5 10 4 63 10 10 5 34 4 8 5 68 5 5 6 37 3 6 6 71 3 3 7 39 2 4 7 73 2 2 8 40 1 2 8 74 1 1 Johnny s mother sends him to the store with $6.00 to spend on apples and grapefruits, and says Son, spend all the cash and be sure to maximize your utility. What will Johnny purchase? Explain. Notice that there are 2 combinations of apples and grapefruit where the equimarginal principle is satisfied: 1. 4 apples and 4 grapefruit (marginal utility per dollar = 10 for each), and 2. 8 apples and 7 grapefruit (marginal utility per dollar = 2 for each). However, only the first of these is within Johnny s budget. 4 apples and 4 grapefruit costs Johnny $2 + $4 = $6. So, the utility maximizing combination in this case is 4 apples and 4 grapefruit. 10. If marginal utility is negative, we can infer that a. Total utility is also negative. b. Total utility is increasing by smaller and smaller amounts. c. The product is an inferior good. d. Total utility is falling. e. The law of diminishing marginal utility does not hold. D 11. Assume leisure is a normal good. The substitution effect of a wage decrease implies a demand for leisure and a labor supply. A. lower; higher B. higher; lower C. higher; higher D. lower; lower A
12. Refer to the figure to the left. If the price of a video game is $9.00, consumer surplus is a. $8.00. b. $9.00. c. $18.00. d. $24.00. e. 6 units f. 5 units P = 9 Q* = 6 CS = ½ (6)(3) = 9 13. True or False: If MU X /P X exceeds MU Y /P Y, then a household can increase its utility by spending more on X and less on Y. TRUE. 14. For a normal good, the income and substitution effect work in the same direction. For an inferior good, the income and substitution effects work in opposite directions. Does this imply that the demand curve for an inferior good is upward sloping? Explain. NO. 15. Assume that Kelly s wage will increase steadily throughout her life. If her wage is less than $20 per hour, the substitution effect of the wage change outweighs the income effect. Once her wage increases above $20 per hour, the income effect begins to outweigh the substitution effect. Graph Kelly s labor supply curve. backward-bending labor supply curve