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University Economics Majors please help! International Trade question?
Problem: If the absolute value of price elasticity of demand in the market is 2 internal and external market is 3, and E (sum) MR = MC = $ 10, calculate at what price the monopolist national international practice of discrimination Price must sell in the domestic market and foreign markets to maximize total profits. Tip: Use the formula MR = P (1-1 / e) of the theory Macroeconomic That's the question I'm having trouble calculating out, any help or typed answer would be a great
We know that a monopoly produces where MR = MC (in this case = $ 10). We also know that total revenue = P * Q. (Explanation of the formula): marginal revenue = DTR / MR = dQ + Q (dP / DQ) Q * (The price is also a function of quantity) MR = P (1 + (dP / dQ) * (Q / P)) (You may recognize the last term as the inverse elasticity of demand) RM = P (1 +1 / e) (Note: mine is + negative and not because the elasticity is generally negative in this case) Since we know that the elasticity domestic demand is -2, we see that MR = P (1 to 0.5) = P / 2 = MC = MR 10 = P / 2 (the establishment of our MR = marginal cost of 10) P = 20 ( in the domestic market) Similarly we know that the elasticity of foreign demand is -3, so: MR = P (1-.33) = 2P / 3 MR = MC = 10 = 2P / 3 P = 15 (on the market external) A some intuition behind the answers: the monopolist to price discriminate always charge a higher price to those where demand elasticities are relatively obtain more inelastic because the quantity demanded will not change much when the price increases. Since domestic demand is relatively inelastic, the monopoly will charges a higher price.
Goldratt on Viable Vision – Theory of Constraints