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A computer company’s cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers), is given by AC = 10 - 0.1Q + 0.3q

  1. Is there a learning-curve effect?

  2. Are there economies or diseconomies of scale?

  3. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.

Short Answer

Expert verified
  1. There exists a learning curve effect.

  2. There are diseconomies of scale.

  3. The average cost of production will decrease in the next year.

Step by step solution

01

Meaning of the learning curve and its relation with the average cost

The learning curve shows a relationship between the cumulative output produced and the amount of input required for each output unit.Since the output produced increases, the requirement for input per unit of output decreases. Thus, both the variables are inversely related. It happens because firms increase their efficiency with experience.

The average cost is the value of inputs per unit of total output produced. The average cost decreases with increasing cumulative output, shown by the negative coefficient of cumulative production in the average cost equation.

Thus, there is a learning curve effect in the company’s cost function.

02

Diseconomies of scale

Diseconomies of scale arise with decreasing returns to scale. Under the diseconomies of scale, the cost of inputs per unit increases with an increase in output.

The cost function of the company shows that as the output produced per year increases, the average cost of the company increases. Therefore, there are diseconomies of scale.

03

Change in average cost of production during the years

Case 1: In the present year:

The cumulative output (Q) is 40, plant size (q) is 10, the average cost is:

AC = 10 – 0.1Q + 0.3q

AC = 10 – 0.1×40 + 0.3×10

AC = 9

Case 2: In the next year:

The plant size (q) is 12, and the cumulative output is 50 (40 + 10). The average cost is:

AC = 10 – 0.1Q + 0.3q

AC = 10 – 0.1×50 + 0.3×12

AC = 8.6

The average cost in the next year will be $8.6 (in thousands), which is $0.4 (in thousands) lesser than this year. Thus, the average cost will decrease next year.

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Most popular questions from this chapter

Suppose that a firm’s production function is q = 10L1/2K1/2. The cost of a unit of labor is \(20 and the cost of a unit of capital is \)80.

  1. The firm is currently producing 100 units of output and has determined that the cost-minimizing quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines.

  2. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this graphically and find the firm’s new total cost.

  3. Graphically identify the cost-minimizing level of capital and labor in the long run if the firm wants to produce 140 units.

  4. If the marginal rate of technical substitution is K/L, find the optimal level of capital and labor required to produce the 140 units of output.

a. Fill in the blanks in the table below.

Units of Output
Fixed Cost
Variable Cost
Total Cost
Marginal Cost
Average Fixed Cost
Average Variable Cost
Average Total Cost
0

100



1

125



2

145



3

157



4

177



5

202



6

236



7

270



8

326



9

398



10

490



b. Draw a graph that shows marginal cost, average variable cost, and average total cost, with cost on the vertical axis and quantity on the horizontal axis.

Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.

The cost of flying a passenger plane from point A to point B is $50,000. The airline flies this route four times per day at 7 am, 10 am, 1 pm, and 4 pm. The first and last flights are filled to capacity with 240 people. The second and third flights are only half full. Find the average cost per passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract—the off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?

Suppose the long-run total cost function for an industry is given by the cubic equation TC = a + bq + cq2 + dq3. Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of a, b, c, and d.

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