Question

1. A firm produces novelty mugs and has a cost function given by C(q) = 50 + 5 × q + 0.5 × q2.

(a) What is the Average Total Cost (ATC) here? What is the Marginal Cost (MC) here? What is the Average Variable Cost (AVC) here?

(b) If the firm is competing in a perfectly competitive market and the current price P = 10, how many mugs does the firm produce? Assuming this is the short run, does the firm make profits here? Does the firm produce here? Use a graph to support your argument.

(c) How many mugs does the firm produce in the long run (Reminder: Firms earn zero profits in the long run, so you need to find the minimum of the ATC)? What price is charged in the long run? What does the long run demand supply curve look like (use words not math)?

(d) If the market demand is given by P = 195?.5×Q, how many firms are in the market in the long run? Give the market supply curve here. How many firms exited or entered the market (i.e. how many firms were producing in the short run versus the long run)?

Answer 1

C(q) = 50 + 5q + 0.5q²

(a)

ATC = C(q)/q = (50/q) + 5 + 0.5q

MC = dC(q)/dq = 5 + q

TVC = 5q + 0.5q²

AVC = TVC/q = 5 + 0.5q

(b) In perfect competition, firm equates price with MC.

5 + q = 10

q = 5

When q = 5,

ATC = (50/5) + 5 + (0.5 x 5) = 10 + 5 + 2.5 = 17.5

AVC = 5 + (0.5 x 5) = 5 + 2.5 = 7.5

Since Price < ATC, firm does not make a profit, but since Price > AVC, firm operates in short run. In following graph, firm equates Price and MC at point A with output q0 (= 5) corresponding to which ATC lies above price but AVC lies below price.

(c) In the long run, Price = ATC = MC.

(50/q) + 5 + 0.5q = 5 + q

0.5q = 50/q

0.5q² = 50

q² = 100

q = 10

Price = MC = 5 + 10 = 15

In the long run, demand curve is horzontal at P = 15 and supply curve is upward rising.

(d) Long run demand: P = 195 - 0.5Q

15 = 195 - 0.5Q

0.5Q = 180

Q = 360

Since q = 10,

Number of firms = Q/q = 360/10 = 36

Firm supply curve is the MC function, so firm supply function: P = 5 + q

Since there are 36 firms in long run, market supply (Qs) = 36 x q, and q = Qs/36

P = 5 + (Qs/36)

36P = 180 + Qs

Qs = 36P - 180 (Market supply curve)

In short run, q = 5, therefore number of firms = 360/5 = 72

So, (72 - 36) = 36 firms did exit the market in long run.