Chapter 7 Word Problem.docx
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Problem 7.1 - Economic profit Problem:
Answer:
After working as a head chef for years, Jared gave up his $60,000 salary to open his own restaurant last year. He withdrew $50,000 of his own savings that had been earning 4% interest and borrowed another $100,000 from the bank at a rate of 5%. As the restaurant space he was leasing had no separate office, Jared converted his basement apartment into office space. He had previously rented the apartment to a student for $300/month. The following table summarizes his operations for the past year.
a.
b.
c. Total sales revenue
$590,000
Employee wages
$120,000
Materials
$350,000
Interest on loan
$5,000
Utilities
$10,000
Rent
$25,000
Total explicit costs a. b.
c.
Jared's accounting profit is the difference between total sales revenue and his explicit costs, or $80,000 in this example. $80,000 = $590,000 – $510,000. Implicit costs include his foregone wages ($60,000), the value of his entrepreneurial skill ($10,000), foregone rent on the apartment ($3,600 = 12 x $300) plus the foregone interest on his savings ($2,000 = .04 x $50,000). These total $75,600. Jared's total economic cost, explicit plus implicit, was $585,600 = $510,000 + $75,600. His economic profit is the difference between revenue and economic cost, or $4,400 (= $590,000 – $585,600).
$510,000
What is Jared's accounting profit? Suppose Jared could have used his talents to run a similar kind of business instead. If he values his entrepreneurial skill at $10,000 annually, find Jared's total implicit costs. What was Jared's economic profit last year?
Problem 7.2 - Total, marginal, and average product Problem:
Answer:
The following table summarizes the short-run relationship between a firm's total labor input and its total output. Labor Input
Total Product
0
0
1
20
2
46
3
75
4
102
Marginal Product
Average Product
a. Labor Input
Total Product
Marginal Product
Average Product
0
0
1 2
20
20
20
46
26
23
3
75
29
25
4
102
27
25.5
5
125
23
25
6
138
13
23
5
125
7
140
2
20
6
138
8
136
-4
17
7
140
8
136
a. b.
c.
Fill in the columns labeled "Marginal Product" and "Average Product." Over what range of labor input does the firm experience increasing marginal returns? Diminishing marginal returns? Negative marginal returns? Comparing marginal product to average product, under what circumstances will average product rise? Under what circumstances will average product fall?
b. c.
d.
Increasing marginal returns corresponds to an increasing marginal product of labor. Marginal product increases through the addition of the third worker. Diminishing returns begins with the addition of the fourth worker, while negative returns appears with the addition of the eighth worker. Average product will rise provided marginal product exceeds average product and fall if marginal product is below average product.
Problem 7.3 - Per-unit cost Problem: Suppose a firm is currently producing 10 units. Its fixed costs are $100 and its variable costs are $40. At an output level of 10 units, what is the firm's current: a. b. c. d. e. f. g.
Total cost? Average fixed cost? Average variable cost? Average total cost? If the total cost of producing 11 units is $147, what is the marginal cost of the eleventh unit? Is average total cost rising or falling? How do you know? Is average variable cost rising or falling? How do you know?
Answer: a. b. c. d.
e.
f.
g.
Total cost (TC) is the sum of total fixed cost and total variable cost. TC = $100 + $40 = $140. Average fixed cost (AFC) is the amount of fixed cost divided by the number of units produced. AFC = $100/10 = $10. Average variable cost (AVC) is the total amount of variable cost divided by the number of units produced. AVC = $40/10 = $4. Average total cost can be found one of two ways. It is the ratio of total cost to total output: ($100 + $40)/10 = $14. It is also the sum of average fixed cost and average variable cost = $10 + $4 = $14. Marginal cost is the increase in total cost associated with the next unit. From part a., the total cost of 10 units is $140. Since the cost of 11 units is $147, the marginal cost of the eleventh unit is $7 = $147 – $140. Average total cost is falling. This is because marginal cost ($7) is less than average total cost ($14). When the cost of the next (marginal) unit is below the average, the average must fall. Average variable cost is rising. This is because marginal cost ($7) is more than average variable cost ($4). When the cost of the next (marginal) unit is above the average, the average must rise.
Answer:
After working as a head chef for years, Jared gave up his $60,000 salary to open his own restaurant last year. He withdrew $50,000 of his own savings that had been earning 4% interest and borrowed another $100,000 from the bank at a rate of 5%. As the restaurant space he was leasing had no separate office, Jared converted his basement apartment into office space. He had previously rented the apartment to a student for $300/month. The following table summarizes his operations for the past year.
a.
b.
c. Total sales revenue
$590,000
Employee wages
$120,000
Materials
$350,000
Interest on loan
$5,000
Utilities
$10,000
Rent
$25,000
Total explicit costs a. b.
c.
Jared's accounting profit is the difference between total sales revenue and his explicit costs, or $80,000 in this example. $80,000 = $590,000 – $510,000. Implicit costs include his foregone wages ($60,000), the value of his entrepreneurial skill ($10,000), foregone rent on the apartment ($3,600 = 12 x $300) plus the foregone interest on his savings ($2,000 = .04 x $50,000). These total $75,600. Jared's total economic cost, explicit plus implicit, was $585,600 = $510,000 + $75,600. His economic profit is the difference between revenue and economic cost, or $4,400 (= $590,000 – $585,600).
$510,000
What is Jared's accounting profit? Suppose Jared could have used his talents to run a similar kind of business instead. If he values his entrepreneurial skill at $10,000 annually, find Jared's total implicit costs. What was Jared's economic profit last year?
Problem 7.2 - Total, marginal, and average product Problem:
Answer:
The following table summarizes the short-run relationship between a firm's total labor input and its total output. Labor Input
Total Product
0
0
1
20
2
46
3
75
4
102
Marginal Product
Average Product
a. Labor Input
Total Product
Marginal Product
Average Product
0
0
1 2
20
20
20
46
26
23
3
75
29
25
4
102
27
25.5
5
125
23
25
6
138
13
23
5
125
7
140
2
20
6
138
8
136
-4
17
7
140
8
136
a. b.
c.
Fill in the columns labeled "Marginal Product" and "Average Product." Over what range of labor input does the firm experience increasing marginal returns? Diminishing marginal returns? Negative marginal returns? Comparing marginal product to average product, under what circumstances will average product rise? Under what circumstances will average product fall?
b. c.
d.
Increasing marginal returns corresponds to an increasing marginal product of labor. Marginal product increases through the addition of the third worker. Diminishing returns begins with the addition of the fourth worker, while negative returns appears with the addition of the eighth worker. Average product will rise provided marginal product exceeds average product and fall if marginal product is below average product.
Problem 7.3 - Per-unit cost Problem: Suppose a firm is currently producing 10 units. Its fixed costs are $100 and its variable costs are $40. At an output level of 10 units, what is the firm's current: a. b. c. d. e. f. g.
Total cost? Average fixed cost? Average variable cost? Average total cost? If the total cost of producing 11 units is $147, what is the marginal cost of the eleventh unit? Is average total cost rising or falling? How do you know? Is average variable cost rising or falling? How do you know?
Answer: a. b. c. d.
e.
f.
g.
Total cost (TC) is the sum of total fixed cost and total variable cost. TC = $100 + $40 = $140. Average fixed cost (AFC) is the amount of fixed cost divided by the number of units produced. AFC = $100/10 = $10. Average variable cost (AVC) is the total amount of variable cost divided by the number of units produced. AVC = $40/10 = $4. Average total cost can be found one of two ways. It is the ratio of total cost to total output: ($100 + $40)/10 = $14. It is also the sum of average fixed cost and average variable cost = $10 + $4 = $14. Marginal cost is the increase in total cost associated with the next unit. From part a., the total cost of 10 units is $140. Since the cost of 11 units is $147, the marginal cost of the eleventh unit is $7 = $147 – $140. Average total cost is falling. This is because marginal cost ($7) is less than average total cost ($14). When the cost of the next (marginal) unit is below the average, the average must fall. Average variable cost is rising. This is because marginal cost ($7) is more than average variable cost ($4). When the cost of the next (marginal) unit is above the average, the average must rise.
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