Jack owns an auto repair shop, specializing in European cars. With three full-ti

Question

Jack owns an auto repair shop, specializing in European cars. With three full-time mechanics, Jack's shop repairs/services 15 cars per week. Each worker is paid $500 per week. By hiring another mechanic, at the same salary, he can increase his weekly output to 20 cars. A fifth mechanic would increase his output to 22, and a sixth one to 23. After hiring the seventh mechanic Jack would see his output drop to 22.

a. Calculate Jack's total variable cost (TVC), marginal cost (MC), and average variable cost (AVC) at these four levels of output.

b. If the average price that Jack charges for each car he services is $500, how many cars per week should he take in? (Explain)

c. Suppose Jack's weekly fixed costs is $1500. Assuming he is a profit maximizer, determine his weekly profit.

d. Does Jack's production function exhibit, constant, increasing, or diminishing returns (to labor)?

Explanation / Answer

Working notes:

(1) Total cost = Total variable cost (Since no fixed costs exist) = $500 x L

(2) AVC = TVC / Q

(3) MC = Change in TC / Change in Q

(4) Total revenue, TR = P x Q = $500 x Q

(5) Profit = TR - TC

So,

(a)

(b) Profit is maximum (= $8500) when Q = 23.

(c) A fixed cost will increase TC by $1500 at every level of output.

Profit is maximized at Q = 22 and 23 when profit = $7000.

(d) Marginal product of labor, MPL = Change in Q / Change in L

So, MPL is falling over entire range of output, signifying diminishing returns to labor.

L Q TC = TVC AVC MC TR PROFIT 3 15 1500 100 7500 6000 4 20 2000 100 100 10000 8000 5 22 2500 113.64 250 11000 8500 6 23 3000 130.43 500 11500 8500 7 22 3500 159.09 -500 11000 7500

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