Assume that a monopolist faces a demand curve for its product given by: p=100−1q Further assume that the firm's cost fun
Posted: Fri Jul 01, 2022 8:19 am
Assume that a monopolist faces a demand curve for its productgiven by:
p=100−1q
Further assume that the firm's cost function is:
TC=570+14q
Use calculus and formulas to find a solution (don't justbuild a table in a spreadsheet as in the previouslesson).
Round the optimal quantity to the nearest hundredthbefore computing the optimal price, which you should also round tothe nearest hundredth. Use these rounded values to compute optimalprofit. Note: Non-integer quantities may make sense wheneach unit of q represents a bundle of many individual items.
Hint 1: Define a formula for Total Revenueusing the demand curve equation.
Hint 2: The first derivative of the totalprofit function, which is cumulative, is the marginal profitfunction, which is incremental. The lecture and formula summaryexplain how to compute the derivative.
Set the marginal profit equal to zero to define an equation forthe optimal quantity q.
Hint 3: When computing the total profitfor a candidate quantity, use the total profit function you define(rather than summing the marginal profits using the marginal profitfunction).
How much output should the firm produce?
Please round your answer to the nearest hundredth.
What price should the monopolist choose to maximizeprofits?
Follow the rounding guidance in the exercise statement for theoptimal quantity when you compute the optimal price. Please roundyour optimal price answer to the nearest hundredth.
What is the profit for the firm at the optimal quantityand price?
Follow the rounding guidance in the exercise statement forquantity and price when you compute the optimal profit. Pleaseround your optimal profit answer to the nearest integer.
p=100−1q
Further assume that the firm's cost function is:
TC=570+14q
Use calculus and formulas to find a solution (don't justbuild a table in a spreadsheet as in the previouslesson).
Round the optimal quantity to the nearest hundredthbefore computing the optimal price, which you should also round tothe nearest hundredth. Use these rounded values to compute optimalprofit. Note: Non-integer quantities may make sense wheneach unit of q represents a bundle of many individual items.
Hint 1: Define a formula for Total Revenueusing the demand curve equation.
Hint 2: The first derivative of the totalprofit function, which is cumulative, is the marginal profitfunction, which is incremental. The lecture and formula summaryexplain how to compute the derivative.
Set the marginal profit equal to zero to define an equation forthe optimal quantity q.
Hint 3: When computing the total profitfor a candidate quantity, use the total profit function you define(rather than summing the marginal profits using the marginal profitfunction).
How much output should the firm produce?
Please round your answer to the nearest hundredth.
What price should the monopolist choose to maximizeprofits?
Follow the rounding guidance in the exercise statement for theoptimal quantity when you compute the optimal price. Please roundyour optimal price answer to the nearest hundredth.
What is the profit for the firm at the optimal quantityand price?
Follow the rounding guidance in the exercise statement forquantity and price when you compute the optimal profit. Pleaseround your optimal profit answer to the nearest integer.