Question

a is 0, b is -1000 i dotn understand the work

3. A perfectly competitive firm sells its product for S100/unit, has $1000 in fixed costs, and has an average variable cost function and a marginal cost function given below: AVC(O)-9-200+500 MC(O)-9-400+500 a. Determine this tim's profit maximizing level of output b. Determine this firm's profits At what level of output would AVC be minimized?

Answer 1

a> At the profit maximizing level, MC=MR

The marginal cost is Q^2-40Q+500

Marginal Revenue is 100

MC=MR

Q^2-40Q+500=100

Q^2-40Q+400=0

(Q-20)^2=0

Q=20

The profit of the firm is 100x20-1000-20^3/3+20*20^2-500*20=-3666.66

But, this is worse than the shutdown case. Because if I shut-down, I will lose the fixed cost which is -1000 and my output would be 0

Thus, most profitable output is 0

b> The profit will be = - Fixed Cost =-1000

c> AVC=Q^2/3-20Q+500

Deriving wrt Q, 2Q/3=20

Q=30

So, min value of AVC is (30^2)/3-20*30+500=200

This is more than the price of 100, thus they should shut down.