Question (1)

A competitive firm sells its product at a price of $0.10 per unit.Its total and marginal cost functions are:

TC = 5 - 0.5Q + 0.001Q2

MC = -0.5 + 0.002Q,

where TC is total cost ($) and Q is output rate (units per time period).

1. Determine the output rate that maximizes profit or minimizes losses in the short term. What is firm's profit at this optimum level?
2. If input prices increase and cause the cost functions to become

TC = 5 - 0.10Q + 0.002Q2

MC = -0.10 + 0.004Q,

what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate when input prices were increased. What is firm's profit?

Question 2

Consider a competitive market in which the market demand for the product is expressed as

P = 75 - 1.5Q,

and the market supply of the product is expressed as

P = 25 + 0.50Q.

Price, P, is in dollars per unit sold, and Q represents rate of production and sales in hundreds of units per day. The firm A in this market has a marginal cost of

MC = 2.5 + 10q.

a. Determine the equilibrium market price and rate of sales (quantity).

b. Determine the firm A's total sales (supply quantities), given your answer to part (a) above.

c. If the market demand were to increase to

Dollar INT Unit MC AC DEAR Q1 Quantity