Assume that a monopolist faces a demand curve for its product given by:p=100−1q
Further assume that the firm’s cost function is:
Using calculus and formulas (don’t just build a table in a spreadsheet as in the previous lesson) to find a solution, how much output should the firm produce at the optimal price?
Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should then round to the nearest cent. 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. Then take the derivative of the Total Revenue and Total Cost formulas to compute the Marginal Revenue and Marginal Cost formulas, respectively. Use these Marginal Revenue and Marginal Cost formulas to perform a marginal analysis.
Hint 2: When computing the total revenue component of total profit for each candidate quantity, use the total revenue function computed from the demand curve equation (rather than summing the marginal revenues using the marginal revenue function).