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Chapter 7: Q3. (page 280)

A firm has a fixed production cost of \(5000 and a constant marginal cost of production of \)500 per unit produced.

  1. What is the firm鈥檚 total cost function? Average cost?

  2. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.

Short Answer

Expert verified

  1. The total cost function is 5000 + 500Q, and the average cost function is 5000Q+500.

  2. The firm will choose to be very large because a large output will minimize the average total cost to $500.

Step by step solution

01

Total cost and average cost function

The total cost function is the fixed cost plus variable cost.

The total variable cost is the product of variable cost per unit (marginal cost) and the total number of units.

Suppose the total units are Q. The total variable cost is:

TVC = MC 脳 Q

TVC = $500Q

The total cost function is:

Total Cost = Total Fixed Cost + Total Variable Cost

Total Cost = 5000 + 500Q

The following formula gives the average cost function:

ATC=TCQATC=5000+500QQATC=5000Q+500

02

Change in output for a minimum average total cost

The total output has to be as maximum as possible to minimize the total cost.The maximum output will reduce the average fixed cost equal to zero.A negligible average fixed cost will result in the average total cost equal to 500, that is, the marginal cost.

Thus, the firm will choose to be maximum to minimize the average total cost.

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Most popular questions from this chapter

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鈥攖he off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output.

  1. How does this tax affect the firm鈥檚 fixed, marginal, and average costs?

  2. 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鈥檚 fixed, marginal, and average costs?

What is the long-run in the microeconomic theory?

Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1000 parking spaces. The firm鈥檚 cost of cement is \(4,000 per acre covered, and its cost of labor is \)12/hour. For the quantities of C and L that the firm has chosen, MPC = 50 and MPL = 4.

  1. Is this firm minimizing its cost of producing parking spaces? How do you know?

  2. If the firm is not cost-minimizing, how must it alter its choices of C and L in order to decrease cost?

In the average cost curve, there is a point where production reaches a minimum. What is that minimum called?
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