Question

Producing robots is a very specialized process which requires special factories.

There are two ways to produce robots (process A and process B).

It turns out that there are exactly 100 locations where you could build a type-A production facility and 100 locations where you could build a type-B facility.

That is, in this industry, there are a maximum of 100 type A firms, and 100 type B firms.

A type "A" firm has production costs: $C_{A}(q)=400 + 80q + q^{2}$ .

A type "B" firm has production costs $C_{B}(q)=800 + 20q + 2q^{2}$ .

These costs are the most efficient way of producing output in the long-run.

Firms in this industry are price takers.

a) What is the long-run equilibrium price and quantity in this market if demand for robots is given by $P(Q)=200-Q/16$?

Answer 1

Given data: - In this Industry there are minimum of 100 type firms, and 100 type B firms. A type 'A' firms has production cost: CA (f) = 400 + 80 g + f^2 A type 'B' firms has production cost: CB (f) = 800 + 20 f + 2 f^2 (a) the long - run Equilibrium price and Quantity in the market demand for robots is given by P(Q) = 200 - Q/16. In long run a perfectly competitive Earn only normal profits. Equilibrium condition P = MC \r\n total cost (A and B) = (400 + 80 f + f^2) + (800 + 20 f + 2f^2) TC = 1200 + 100 g + 3f^2 MC = 100 + 6 f A. p = 200 - f/16 O = MC 3200 - f/16 = 100 + 6 f 3200 - f = 1600 + 96 f 97 f = 1600