A monopolist produces output and sells it in two distinct markets, with revenue functions R1 & R2. The total cost of producing the output y1 for market 1 and y2 for market 2 is C (y1 + y2)
(1) Show that a profit maximizing monopolist equates marginal revenue in each market to the common marginal cost.
(2) Derive mathematically the formulas for the price-elasticity of demand and for the income-elasticity of demand. Interpret both measures (for example, assume that the price-elasticity of demand is -1.5 and write a sentence with this number.)
(3) Given a revenue function R (y), the average price for selling y units of output is p(y) = R(y) / y. Recall that elasticity of demand E is defined by
E(y) = -p(y)/yp'(y)
Show that R'(y) = p(1- 1/E(y)) and that the monopolist's price is higher in the market with the less elastic demand