Question

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.

1. Find total profit function, and find the first derivative of total profit with respect to quantity.
2. What is the optimal price to sell these MacroCon Newsletters?
3. If the price were $394 and the number of newsletters sold by MacroCon was 187, would MacroCon be profitable?

Answer 1

Q = 581 - P
So, P = 581 - Q

a. Profit = Total revenue - TC = P*Q - (35 + 20Q + 0.5Q²) = (581-Q)*Q - 35 - 20Q - 0.5Q² = 581Q - Q² - 35 - 20Q - 0.5Q²
So, = 561Q - 1.5Q² - 35

First derivative:

b. First derivative = 0
So, 561 - 3Q = 0
So, 3Q = 561
So, Q = 561/3 = 187

P = 581 - Q = 581 - 187 = 394
So, optimal price = $394

c.

So, profit is maximum when price = $394 and quantity = 187. Thus, MacroCon would be profitable.

Profit = 561Q - 1.5Q² - 35 = 561(187) - 1.5(187)² - 35 = 104,907 - 52,453.5 - 35 = 52,418.5