Question

1. A manufacturing company produces and sells small farm tractors. Its annual fixed costs are $15 million, and its marginal cost per tractor is $20,000. Demand for small tractors is given by:

P = 30,000 – Q, where P denotes price in dollars and Q is annual sales.

MR = 30,000 – 2Q = 20,000

(a) Find the firm's profit-maximizing output, price, and annual profit.

(b) Assume that agriculture prices fall and the farming sector faces a mild recession. The demand for the small tractors drops to:

P = 26,000 – Q.

MR = 26,000 – 2Q

Suppose the recession is only temporary, and demand will recover soon. What price and output adjustment should the firm make during the recession?

Answer 1

Provided that fixed costs, F = $15,000,000

Marginal cost per tractor, MC = $20,000

Demand is given as, P = 30,000 - Q

P is the price in dollars and Q is annual sales

Marginal Revenue is given as, MR = 30,000 - 2Q

(a). For profit-maximising, MR = MC, such that,

30,000 - 2Q = 20,000

2Q = 10,000

Q = 5,000

Now putting this value in demand function,

P = 30,000 - Q

P = 30,000 - 5,000

P = $25,000

These are the firm's profit-maximizing output and price.

Annual profit can be computed as,

Profit = Revenue - Cost

= PxQ - F - MCxQ

= (25,000)x(5,000) - (15,000,000) - (20,000)(5,000)

= 125,000,000 - 115,000,000

= $10,000,000

(b). The new demand function is given as,

P = 26,000 - Q

MR = 26,000 - 2Q

The firm will adjust for profit-maximizing output, which will be computed as,

MR = MC

26,000 - 2Q = 20,000

2Q = 6,000

Q = 3,000

Putting this in the demand function to obtain the profit-maximizing price,

P = 26,000 - Q

P = 26,000 - 3,000

P = $23,000

These are the profit-maximizng output and prices.