Show a profit maximizing monopolist equates marginal revenue

Reference no: EM13182875

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

Reference no: EM13182875

Questions Cloud

What is the producers optimal profit as a function : A producer produces good y using inputs x1 and x2 according to the production function y = x1^(alpha)x2^(beta) where alpha + beta

What is the optimal profit function of the firm : A firm has cost function: C(y) = { y^2 + 1 if y > 0, {0 if y = 0, Let p be the price of output. 1) If p = 2, how much will the firm produce? If p = 1, how much will the firm produce? 2) What is the (optimal) profit function of the fir..

What is the long-run supply for the firm : A firm has a long-run cost function C1(y) = y^3 - 10y^2 + 30y. 1) Derive the firm's long-run average cost function 2) Derive the firm's long-run marginal cost function 3) Find the level of production with the lowest average cost 4) What is..

What is the minimum number of moles of sodium hydroxide : what is the minimum number of moles of sodium hydroxide required of this hydrolysis reaction to go to completion and what is the limiting reagent in this experiment?

Show a profit maximizing monopolist equates marginal revenue : (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 m..

State the ethanol boiled off prior to extraction : the Fischer esterification experiment why was the majority of the ethanol boiled off prior to extraction and why was the reaction vial cooled

What are the first and second-order condition for the profit : A producer produces good y using a single input x according to the production function y=x^a where 0

State what molar amount of hydrochloric acid : What molar amount of hydrochloric acid is required for the fischer esterification of lauric acid

When the multifibre agreement-mfa expired : Suppose that in Question 1, the government rather than using a tariff, decides to limit the quantity of imports to 4. All the quota licenses are given to the nephew of the minister of finance (no rent seeking). Show on a new graph the outcome of t..

User Account

All Pages