Question

QUESTION 3 126 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 0.5Q2 20Q+ a. Find total profit function, and find the first derivative of total profit with respect to quantity. 2 Marks] b. What is the optimal price to sell these MacroCon Newsletters? 1 Markl c. If the price were $394 and the number of newsletters sold [1 Markl Total: 10 Marks] by MacroCon was 187, would MacroCon be profitable?

Answer 1

Demand for the newsletter, Q = 581 - P Q rightarrow no.of newsletter sold P rightarrow Price TC = 35 + 20Q + 0.5 Q^2 total revenue, TR = P.Q = (581 - Q) Q Total Profit function = TR - TC = 581 Q - Q^2 - 35 - 20Q - 0.5 Q^2 = 561 Q - 1.5 Q^2 - 35 it derivative of total profit with respect its quantity = 561 - 3Q Calculate optimal price, Marginal revenue = marginal cost d(f_R)/dq = d(Tc)/dQ = > 581 - 2Q = 20 + Q 561 = 3Q Q = 1.87 P = 581 - Q = 394 optimal price = $394 P = $394 Q = 187 profit = 561Q - 1.5Q^2 - 35 = 52418.8 Yes, it will be profitable