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Suppose the cost of producing q cars is given by c(q) = 7500 +2000q-10q^2

a. What is the variable cost of producing 10 cars?

b. What is the marginal cost of producing the 10th car?

c. Solve for AC(q) and AVC(q) and are they increasing?

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Ronald
RonaldLv2
28 Sep 2019

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Related questions

Suppose that a competitive firm's marginal cost of producing output q is given by MC (q) = 3 + 2q. Assume that the market price of the firm’s product is $9. a. What level of output will the firm produce? b. What is the firm’s producer surplus? c. Suppose that the average variable cost of the firm is given by AVC (q) = 3 + q. Suppose that the firm's fixed costs are known to be $3. Will the firm be earning a positive, negative, or zero profit in the short run?

3. A firm has a long-run production function:   

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run? 

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

14 At a total cost of $300, Jill's Toys can produce 10 toy cars an hour, at a total cost of $370, Jill's Toys can produce 11 toy cars per hour. Jill's Toys has an average fixed cost equal to $25 when the company is producing 10 toy boats per hour. Which of the following is true? A. The marginal cost of going from the tenth to the eleventh toy car is $70. B. The average total cost is more than the marginal cost of producing the eleventh toy car. C. The average variable cost is more than the marginal cost of producing eleventh toy car. D. The total variable cost of producing 10 toy boats is $30. E. None of these answers are true.

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