Question

The short run cost function of a firm is as follows: total cost=200+5Q+2Q^2 :where Q=physical units of the product of the firm. What would be the level of optimum output ?

Answer 1

N.B. Presumably, this question is about a firm operating in a competitive market, since it contains no information about the impact of the produced units on the market price.

Answer:

A firm's production level reaches its optimum and hence maximizes profit when the firm produces where marginal revenue equals marginal costs, i.e. MR=MC (1)
In a competitive market any particular firm is a price-taker and, therefore, MR=P and (1) becomes MC=P.

Calculate marginal cost:

MC = dTC / dQ
MC = d(200+5Q+2Q^2) / dQ
MC = 5+4Q

Therefore:

MC = P
5 + 4Q = P
Q = (P - 5) / 4

where P is the price of a physical unit of the product.