Assume that a monopolist faces a demand curve for its product given by: p = 80 – 2q Further assume that the firm's cost function is: ТC — 560 + 13q Use calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson). Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should also round to the nearest hundredth. Use these rounded values to compute optimal profit. Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items. Hint 1: Define a formula for Total Revenue using the demand curve equation. Hint 2: The first derivative of the total profit function, which is cumulative, is the marginal profit function, which is incremental. The lecture and formula summary explain how to compute the derivative. Set the marginal profit equal to zero to define an equation for the optimal quantity q. Hint 3: When computing the total profit for a candidate quantity, use the total profit function you define (rather than summing the marginal profits using the marginal profit function). How much output should the firm produce? Please round your answer to the nearest hundredth.

Assume that a monopolist faces a demand curve for its product given by: p = 80 – 2q Further assume that the firm's cost function is: ТC — 560 + 13q Use calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson). Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should also round to the nearest hundredth. Use these rounded values to compute optimal profit. Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items. Hint 1: Define a formula for Total Revenue using the demand curve equation. Hint 2: The first derivative of the total profit function, which is cumulative, is the marginal profit function, which is incremental. The lecture and formula summary explain how to compute the derivative. Set the marginal profit equal to zero to define an equation for the optimal quantity q. Hint 3: When computing the total profit for a candidate quantity, use the total profit function you define (rather than summing the marginal profits using the marginal profit function). How much output should the firm produce? Please round your answer to the nearest hundredth.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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