Suppose the market demand for milk is Additionally,suppose that a dairy's variable costs are (where Q is the number of gallons of milk produced each day),its marginal cost is 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?
A) 50
B) 5
C) 10
D) 20

Question

Suppose the market demand for milk is  Additionally,suppose that a dairy's variable costs are  (where Q is the number of gallons of milk produced each day),its marginal cost is  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?
A) 50 
B) 5 
C) 10 
D) 20

Quizplus · Accepted Answer

To determine the number of active firms in the market, we need to first calculate the market supply. Since there is free entry into the market, firms will enter until economic profits are zero.

To find the supply curve at zero economic profit, we need to set price equal to marginal cost (P=MC).

From the demand equation, we know that at P=$2, Q=1100. Therefore, setting P=$2, we get:

1100 = -50 + Q * (2 - 0.001Q) - 0.0002Q^2

Simplifying:

0.0002Q^2 - 2Q + 1150 = 0

Using the quadratic formula:

Q = (2 ± sqrt(4 - 4(0.0002)(1150))) / (2 * 0.0004)

Q = 500, 3500

Since Q represents the number of gallons produced by a single firm, we need to divide these quantities by the output per firm:

Q per firm = 3500 / N

Where N is the number of active firms.

Setting this equal to the marginal cost:

2 = 1 + 0.0002(3500/N)

0.0002(3500/N) = 1

N = 10

Therefore, there are 10 active firms in the market.

Suppose the Market Demand for Milk Is Additionally,suppose That