Answer to Question #314704 in Microeconomics for Cheu Soeur Lonh

Question

A locomotive producer’s demand function is P1 = 18 – 0.6Q for price increases and

P2 = 20 - 0.8Q for price decreases. The marginal cost is constant and equal to 5.

a. What price is the firm now charging and how much output is being produced?

b. If marginal cost increase to 6, how much would the firm produce?

c. If marginal cost decreases to 3, how much would the firm produce?

Answer 1

The price multiplied by the quantity will give us the total revenues in each case.

$(18 – 0.6Q)Q$

The total revenue in this case is;

$18Q-0.6Q^2$

In the second case

$(20−0.8Q)Q$

$20Q-0.8Q^2$

At optimum production, Marginal cost and marginal revenue are equal and in the cases above, the marginal cost is constant therefore we pick one equation.

$\frac{\Delta TR}{\Delta Q} =20-1.6Q$

$20-1.6Q = 5$

$-1.6Q =-15$

$Q= 9.375$

a) At marginal cost of 5 ( this indicates price decrease) therefore we use

$P2 = 20(9.375) – 0.8(9.375)^2$

$P2=117.1875$

$Q= 9.375$

b) If the marginal cost increases to 6 we use the other equation