Question

Each firm in a competitive market has a cost function​ of: Upper C equals 25 plus q squared​, so its marginal cost function is MC equals 2 q. The market demand function is Upper Q equals 35 minus p. Determine the​ long-run equilibrium​ price, quantity per​ firm, market​ quantity, and number of firms.

Answer 1

Answer and Explanation:

The computation is shown below:

TC = 25 + q^2

Now

Marginal cost is

= dtc ÷ dQ

= 2q

Average variable cost  (AVC) = q

We Assuming perfect competition so there is a free entry so no profits

Therefore

ATC = P

ATC = TC ÷ q  

= q + 25 ÷ q

Now

MC = MR = P = ATC

2q = q + 25 ÷ q

q = 25 ÷ q

q^2 = 25

So, Quantity per firm = q = 5

Now

P = MC = MR = ATC

= q + 25 ÷ q  

= 5 + 25 ÷ 5  

= 5 + 5

= 10

hence, equilibrium price is 10

Now

Q = 35 - P  

= 35 – 10

= 25

Hence, Market quantity (Q)  = 25

And, the number of firms i.e n

N = Q ÷ q  

= 25 ÷ 5

= 5