Chapter 8 How Firms Make Decisions: Profit Maximization
CHAPTER 8 - HOW FIRMS MAKE DECISIONS:
PROFIT MAXIMIZATION
ANSWERS TO EVEN-NUMBERED problemS
2. a. Annual explicit costs:
cost of office equipment: $3,600
programmer’s salary: 25,000
heat and light: $50 12 = 600
total explicit costs: $29,200
b. Annual implicit costs:
salary foregone: $35,000
investment income
foregone: $10,000 .05 = 500
rent foregone: $250 12 = 3,000
total implicit costs: $38,500
c. Congratulations are not in order since economic profit for the year is
$55,000 – ($29,200 + $38,500) = –$12,700.
4. The profit-maximizing level of output is 14. As the firm chooses to produce the 11th, 12th and 13th unit MR>MC so it is clear that they should continue to increase their quantity and thereby increase profits. As the firm considers the production of the 14th unit they see that MR=MC, i.e. they cannot make any additional profit by producing the 14th unit. Hence, we deduce that the firm is indifferent between producing 13 or 14 units because their overall profit is the same. They would definitely not produce the 15th unit as MR<MC, which indicates that they would earn negative profit on the 15th unit, or equivalently that their overall profit would be lower if they produced 15 units than if they produced 14.
6. If the firm’s fixed costs are $3,000 per day, then its variable costs are $7,000 - $3,000 = $4,000 per day. Since its total revenue is less than this amount, this firm should shut down in the short run.
b. Since the firm is earning enough total revenue to cover these variable costs, it should continue to operate in the short run.
8. a. The tax hike does not affect Ned’s MC and MR curves.
b. Ned should continue to produce 5 beds in the short run.
10. a. When price falls from $450 to $400, quantity rises from 5 to 6 units per day.
%∆P = ($400 - $450) / $425 = -11.8%.
%∆Q = (6 – 5) / 5.5 = 18.2%.
ED = 18.2% / 11.8% = 1.54
When price falls from $400 to $350, quantity rises from 6 to 7 units per day.
%∆P = ($350 - $400) / $375 = -13.3%.
%∆Q = (7 – 6) / 6.5 = 15.4%.
ED = 15.4% / 13.3% = 1.16.
When price falls from $350to $300, quantity rises from 7 to 8 units per day.
%∆P = ($300 - $350) / $325 = -15.4%.
%∆Q = (8 – 7) / 7.5 = 13.3%.
ED = 13.3% / 15.4% = 0.86
b. In Table 1, Total revenue rises when output rises from 5 to 6, and from 6 to 7. These are the output changes for which demand was found to be elastic (ED > 1) in part a. When demand is elastic, a drop in price (and a rise in quantity) should increase total revenue. So the rise in total revenue is consistent with the elasticities.
Total revenue falls when output rises from 7 to 8. For this output change, demand was found to be inelastic (ED < 1) in part a. When demand is inelastic, a drop in price (and a rise in quantity) should decrease total revenue. So the behavior of total revenue is once again consistent with the elasticities.
c. In Table 1, marginal revenue is positive when output rises from 5 to 6, and from 6 to 7. These are the output changes for which demand was found to be elastic (ED > 1) in part a. When demand is elastic, a drop in price (and a rise in quantity) should increase total revenue, which means marginal revenue should be positive. So these values for marginal revenue are consistent with the elasticities.
Marginal revenue is negative when output rises from 7 to 8. For this output change, demand was found to be inelastic (ED < 1) in part a. When demand is inelastic, a drop in price (and a rise in quantity) should decrease total revenue, which means marginal revenue should be negative. So the value of marginal revenue is once again consistent with the elasticities.
12. a. Over the short run (a few months), the bakery’s TFC = $4,000 per month, and its TVC = $1 x 5,000 = $5,000 per month, so TC = TFC + TVC = $4,000 + $5,000 = $9,000. The bakery’s total revenue is $1.50 x 5,000 = $7,500 per month. So monthly profit = TR – TC = $7,500 - $9,000 = -$1,500 (a monthly loss of $1,500).
b. Over the short run (for the next few months), the bakery should keep operating, because TR of $7,5000 is greater than TVC of $5,000. Staying open gives the bakery an operating profit, and helps it pay its fixed costs.
c. If the bakery’s current plant is also its least cost plant, it will not be able to reduce costs in the long run. Since it will be suffering a long-run loss, it should exit the industry in the long run (i.e., after a year has passed and its lease runs out).
14. To answer this question, we need to compare the marginal revenue and marginal cost of the action. Marginal cost can be computed from average total cost by first computing total cost.
Unit / ATC / TC / MC74 / $10,000 / $740,000
$160,000
75 / $12,000 / $900,000
$164,000
76 / $14,000 / $1,064,000
The marginal cost for the 76th unit is $164,000. Marginal revenue of the 76th unit is what Backus Electronics is offering to pay for it, or $150,000. Howell should not accept the offer since marginal cost exceeds marginal revenue.