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Chapter 7: Problem 9

The short-run cost function of a company is given by the equation \(\mathrm{TC}=200+55 q\), where \(\mathrm{TC}\) is the total cost and \(q\) is the total quantity of output, both measured in thousands. a. What is the company's fixed cost? b. If the company produced 100,000 units of goods, what would be its average variable cost? c. What would be its marginal cost of production? d. What would be its average fixed cost? e. Suppose the company borrows money and expands its factory. Its fixed cost rises by \(\$ 50,000\), but its variable cost falls to \(\$ 45,000\) per 1000 units. The cost of interest ( \(i\) ) also enters into the equation. Each 1 -point increase in the interest rate raises costs by \(\$ 3000 .\) Write the new cost equation.

Short Answer

Expert verified
a) The company's fixed cost is $200,000; b) The average variable cost for 100,000 units of goods is $55; c) The marginal cost of production is $55; d) The average fixed cost for 100,000 units of goods is $2; e) The new cost equation is TC = (200 + 50 + 3i) + 45q.

Step by step solution

01

Fixed and Variable Costs

The total cost equation is given as TC = 200 + 55q. Here, 200 represents the fixed costs of the company (in thousands). The variable cost is represented by the 55q term, where q is the quantity of output.
02

Average Variable Cost

To find the average variable cost(AVC), the equation is AVC = Variable Cost / Quantity. Here, the variable cost is 55q, and for 100,000 units (or 100 in thousands), the AVC = 55q / q = 55.
03

Marginal Cost

The marginal cost is obtained by differentiating the total cost function with respect to quantity. Here, the derivative of 55q is 55. Hence the marginal cost is 55.
04

Average Fixed Cost

The average fixed cost(AFC) is calculated as AFC = Fixed Cost / Quantity. Here, the fixed cost is 200 so AFC for 100,000 units of goods (or 100 in thousands) is AFC = 200/100 = 2.
05

New cost equation

It is mentioned that fixed cost rises by $50,000 (or 50 in thousands) and variable cost falls to $45,000 per 1000 units (or 45). The new cost equation includes interest rate (i) which increases costs by $3000 per unit increase in 'i'. Therefore, the new total cost function is TC = (200 + 50 + 3i) + 45q.

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Most popular questions from this chapter

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 \\[\mathrm{AC}=10-0.1 Q+0.3 q\\] a. Is there a learning-curve effect? b. Are there economies or diseconomies of scale? c. 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.

A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units \(H\) and software programs \(S\) is given by \\[\mathrm{TC}=a H+b S-\mathrm{cHS}\\] where \(a, b,\) and \(c\) are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? With economies or diseconomies of scope?

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. a. How does this tax affect the firm's fixed, marginal, and average costs? b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm's fixed, marginal, and average costs?

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.

A recent issue of Business Week reported the following: During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That's because closing and reopening plants is expensive, partly because the auto makers' current union contracts obligate them to pay many workers even if they're not working. When the article discusses selling cars "at a loss," is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly.
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