Question

You are considering starting your own economic consulting operation, which you plan to call MacroCon Sdn Bhd. Your firm will “sell” economic newsletters that foretell the macroeconomic future for Gross National Product (GNP), interest rates, stock prices, gold prices, and the value of the dollar versus the Yen.

Demand for the MacroCon Newsletter is expected to be: Q = 581 – P, where Q is the number of newsletters sold and P is the price. The costs of producing newsletters is:

TC = 35 + 20Q + 0.5Q2.

a. Find total profit function, and find the first derivative of total profit with respect to quantity.

b. What is the optimal price to sell these MacroCon Newsletters?

c. If the price were $394 and the number of newsletters sold by MacroCon was 187, would MacroCon be profitable?

Answer 1

Answer

a)

Profit = Total Revenue(TR) - Total Cost(TC)

TR = P*Q = (581 - Q)Q

Hence,

Profit = (581 - Q)Q - (35 + 20Q + 0.5Q²)

First Derivative is given by:

d(Profit)/dQ = 581 - 2Q - (20 + Q)

b)

In order to maximize profit function defined above we have to set First derivative = 0

=> d(Profit)/dQ = 581 - 2Q - (20 + Q) = 0

=> 561 = 3Q

=> Q = 187

Hence Profit Maximizing quantity = 187

So P = 581 - Q = 581 - 187 = 394

Hence Profit Maximizing Price = 394

c)

Using Profit function defined in part (a) , when Price = 394 and Quantity = 187

Profit = (581 - Q)Q - (35 + 20Q + 0.5Q²) = (581 - 187)*187 - (35 + 20*187 + 0.5*187²) = 52418.5

Hence,

Profit = 52418.5 which is greater than 0

Hence, MacroCon would be Profitable