Question

If your firm has a total cost function equal to: C(Q) = 15,000 + 50Q + 0.2Q² , what is the marginal cost of producing the 30th unit of output (Q)?

A firm has a Leontief production function: Q = min{8K, 4L}. A unit of capital costs the firm $10 and each worker costs $15. If the firm is producing 320 units of output at the lowest possible cost, what is their average total cost (of producing 320 units of output)?

Answer 1

1)

C(Q) = 15000 + 50Q + 0.2Q2

MC = 50 + 0.4Q

Q = 30

MC = 50 + 0.4(30)

MC = 50 + 12 = 62

So MC of producing 30th unit of output is 62

2)

Q = min{8K,4L}

capital cost = r = 10

worker cost  = w = 15

Q = min{8K,4L}

Q = 8K  

Q/8 = K  

Q = 4L

Q/4 = L  

Total cost C = wL + rK  

C = 15(Q/4) + 10(Q/8)

C = 15Q/4 + 5Q/4

C = (15Q + 5Q)/4

C = 20Q/4

C = 5Q

ATC = C/Q

ATC = 5Q/Q

= 5

Q = 320

Total cost C = 5Q = 5(320) = 1600

ATC = 5