Suppose the market demand for milk is Q^d = 150

Question

Suppose the market demand for milk is Q^d = 150 - 5P.Additionally,suppose that a dairy's variable costs are VC = 2Q² (where Q is the number of gallons of milk produced each day),its marginal cost is MC = 4Q and there is an avoidable fixed cost of $50 per day.In the long run there is free entry into the market.How many active firms are in the market?

Quizplus · Accepted Answer

In long run equilibrium, each firm will produce at the minimum point of its average variable cost curve, which is where MC = AVC. 
Thus, 4Q = 2Q^2/U1P12. Simplifying this equation, we get Q = 40. 
Substituting Q = 40 into the demand equation, we get P = $22. 
At this price, each firm will produce 40 gallons of milk, and will earn a profit equal to (P - AVC) * Q - FC. 
AVC = 2(40)^2/U1P12 = $0.50 per gallon. 
The profit equation for each firm then becomes (22-0.50)*40-50=$770. 
The total quantity supplied in the market is 400 gallons. 
Thus, the number of firms in the market is 400/40 = 10.

Suppose the Market Demand for Milk Is Qd = 150