Question

1. There are four competitive, profit-maximizing firms in the Bozeman craft brewing market: Bozeman Brewing Company, Bridger Brewing, Outlaw Brewing, and 406 Brewing Company. Suppose these four firms are price takers and have the same cost function: C(qi) = 600 + 20qi + 2qi2 where qi is output of firm i measured in kegs. Each firm can sell its output for $100 per keg. Write down the profit function for one of these firms. What is its marginal cost function? What is its average variable cost function?

2. Assuming firms produce, how many kegs will each profit-maximizing firm produce? What is the total profit earned by each firm at this quantity?

3. Suppose that fixed costs are sunk in the short run. Given the profit-maximizing level of output, should these breweries shut down in the short run? Why or why not?

4. Below what price would brewers in this market choose to shut down?

5. What is the market supply function (Qs(p)) of Bozeman craft beer? (Don’t forget to indicate when supply is zero).

6. Suppose the Bozeman municipal government announces a change in alcohol licensing. A new licensing fee of $400 will be imposed on brewers. Will the brewers pay the fee and continue operating or shut down?

Answer 1

1. Profit function of Firm 1 (Bozeman brewing company) :

P*q₁ - C(q₁) = 100q₁ - 600 - 20q₁ - 2q₁² = 80q₁ - 600- 2q₁²

MC(q₁) = 20 + 4q₁ ( Differentiating C(q₁) wrt to q₁)

AC(q₁) = TC/q₁ = 600/_q1 + 20 + 2q₁

2.Equilibrium condition is given by P=MC

100= 20 + 4q₁

q₁ = 20, each firm will produce 20 units

Profits earned by each firm: 80*20 - 600 - 2(20)²

= 1600 - 600 - 800 = 200

3. The short run shut down point for the breweries in a competitive market is at the minimum of AVC curve.

Variable Cost = 20q₁ + 2q₁²

AVC = 20 +2q₁

Minimum of this curve is 20 since q₁ cannot be negative. Thus, breweries won't shutdown in the short run since P>AVC

4. Brewers in this market will shut down when the price falls below $20