Economics (McConnell) AP Edition, 19th Edition

Chapter 7: Businesses and the Costs of Production

Worked Problems

Problem 7.1 - Economic profit

Problem:

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.

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

 

$510,000

  1. What is Jared's accounting profit?
  2. 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.
  3. What was Jared's economic profit last year?

Answer:

  1. 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.
  2. 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.
  3. 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).


Problem 7.2 - Total, marginal, and average product

Problem:

The following table summarizes the short-run relationship between a firm's total labor input and its total output.

Labor Input

Total Product

Marginal Product

Average Product

0

0

 

 

1

20

 

 

2

46

 

 

3

75

 

 

4

102

 

 

5

125

 

 

6

138

 

 

7

140

 

 

8

136

 

 

  1. Fill in the columns labeled "Marginal Product" and "Average Product."
  2. Over what range of labor input does the firm experience increasing marginal returns? Diminishing marginal returns? Negative marginal returns?
  3. Comparing marginal product to average product, under what circumstances will average product rise? Under what circumstances will average product fall?

Answer:


  1. Labor Input

    Total Product

    Marginal Product

    Average Product

    0

    0

     

     

    1

    20

    20

    20

    2

    46

    26

    23

    3

    75

    29

    25

    4

    102

    27

    25.5

    5

    125

    23

    25

    6

    138

    13

    23

    7

    140

    2

    20

    8

    136

    -4

    17


  2. 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.
  3. 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:

  1. Total cost?
  2. Average fixed cost?
  3. Average variable cost?
  4. Average total cost?
  5. If the total cost of producing 11 units is $147, what is the marginal cost of the eleventh unit?
  6. Is average total cost rising or falling? How do you know?
  7. Is average variable cost rising or falling? How do you know?

Answer:

  1. Total cost (TC) is the sum of total fixed cost and total variable cost. TC = $100 + $40 = $140.
  2. Average fixed cost (AFC) is the amount of fixed cost divided by the number of units produced. AFC = $100/10 = $10.
  3. Average variable cost (AVC) is the total amount of variable cost divided by the number of units produced. AVC = $40/10 = $4.
  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.
  5. 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.
  6. 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.
  7. 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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