Question

Picton Petticoats sells its product at a price of £15 each (the demand curve is horizontal at this price). Its total and marginal cost functions are: T C = 50 − q + 0.01q 2 MC = −1 + 0.02q, where T C and MC are measured in £, and q is output rate (petticoats per day). (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 petticoats increases to £18, effectively shifting the demand curve up to that level. How does this change Picton’s optimal output decision? (d) Suppose that workplace safety regulations are imposed that effectively raise the total cost function to: 50 − q + 0.02q 2 . How does the optimal output level change if the output price remains at £15?

Answer 1

The equilibrium point is where the marginal cost (MC) is equal to the price

MC = – 1 + 0.02q; where q is the output

Price (P) = £15

Part 1) Equating price and MC

15 = – 1 + 0.02q

16 = 0.02q

Equilibrium output = 800

Part 2) Profit = Total Revenue (TR) – Total Cost (TC)

TR = Price × Output

TR = 15 × 800

TR = 12,000

TC = 50 – q + 0.01q²

TC = 50 – 800 + 0.01(800)²

TC = 5,650

Profit = 12,000 – 5,650

Profit = £6,350

Part c) Now it is given that the price of petticoats has increased to £18

Equating price and MC

18 = – 1 + 0.02q

19 = 0.02q

Equilibrium output = 950

Part d) It is given that the price is £15, but the new total cost function is following

TC = 50 – q + 0.02q²

MC = ∆TC/∆q = – 1 + 0.04q

Equating price and MC

15 = – 1 + 0.04q

16 = 0.04q

Equilibrium output = 400