Question

Cafe Caffe sells its product at a price of €5 each (the demand curve is horizontal at this price). Its total and marginal cost functions are: TC = 50 - 4+0.019? MC = -1 +0.024 where TC and MC are measured in €, and q is the output rate. (a) Determine the output rate that maximizes profit or minimizes losses in the short run. (b) Calculate the profit earned at the output level you calculated in (a). (c) Suppose that the price of caffe increases to €8, effectively shifting the demand curve up to that level. How does this change Cafe Caffe's optimal output decision? (d) Suppose that workplace safety regulations are imposed that effectively raise the total cost function to: 50 - 9 +0.027?. How does the optimal output level change if the output price remains at €5?

Answer 1

(a) Profit maximization condition for short-run under Perfect competition : P = MC

5 = -1+0.02q

0.02q=6

q=600/2=300

Thus, in short-run profit-maximization level of output is q=300

(b) Profit earned = TR - TC = PQ - (50-q+0.01q^2)

Profit = 5*300 - (50-300+0.01*300*300)

Profit = 1500 - (650) = 850

(c) Now P=8

Short-run equilibrium condition is: P = MC

8=-1+0.02q

0.02q=9

q=900/2=450

Thus, optimal output increase from 300 to 450

(d) New TC = 50-q+0.02q^2

New MC = -1+0.04q

P=5

Short-run equilibrium condition under Perfect competition: P = MC

5=-1+0.04q

0.04q=6

q=600/4 = 150

Thus, optimal output is 150, that is decrease by 150 from the level of 300 at P=5 when TC changes from TC=50-q-0.01q^2 to TC=50-q-0.02q^2