Answer to Question #178170 in Microeconomics for Dawit

Question

1.       Assume that you are working in one of the profit marking firm in town as a research and planning expert. Your organization faces a cost function of C(Q) = 3Q² + 10Q + 50; and the demand function for the product the firm produces Q = 125 - 5P. If your firm is going to a pricing decision which enable it to maximize its profit. How much price you are expected to advice for the decision maker?

2.      A firm faces a non-linear demand function of P = 250 - 3Q₁³ - Q₁² + Q₂²  + Q₁ - Q₂ for two products is the same. Compute the marginal revenue for each product. 

Answer 1

1.

product demand equation

$Q=125-5P$

$\therefore P=25-0.2Q$

$TC=3Q^2 + 100Q+ 50$

$MC=6Q+100$

$TR=Q(25-0.2Q)$

$=25Q-0.2Q^2$

$MR=25-0.4Q$

To find Q at which MR=MC

$25-0.4Q=6Q+100$

$-75=6.4Q$

$Q=-11.71875$

The  negative output  means that there is slack in the economy due to weak demand.

Price associated with Q=-11.71875

$P=25-0.2(-11.71875)$

$P=22.65625$

I would advice price to be set at 22.65625

2.

$MR=\frac{\Delta TR}{\Delta Q}$

Marginal product for Q₁

$\frac{\Delta TR_1}{Q_1}=\frac{250Q_2-3Q_1 ^3Q_2-Q_1^2Q_2+Q_2^3+Q_1Q_2-Q_2^2}{\Delta Q_1}$

$=-9Q_2Q_1^2-2Q_2Q_1+3Q_2^2+Q_1-2Q_2$

Marginal product for Q₂

$\frac{\Delta TR_2}{Q_2}=\frac{250Q_2-3Q_1 ^3Q_2-Q_1^2Q_2+Q_2^3+Q_1Q_2-Q_2^2}{\Delta Q_2}$

$=250-3Q_1^3-Q_1^2+3Q_2^2+Q_1-2Q_2$