# HW4solution - Micro 3101 Solution to Homework Assignment 4...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Micro 3101 Solution to Homework Assignment 4 Monopoly 1. (a) To find the Marginal Revenue, we first have to ”invert” the demand function to the inverse demand function as P = 100- Q. The total revenue is then TR ( Q ) = P × Q = 100 Q- Q 2 . Differentiating TR with respect to Q , we have MR ( Q ) = 100- 2 Q. Marginal cost is the derivative of TC with respect to Q , which is MC ( Q ) = Q + 10 . Average cost is just total cost divided by Q , which is AC ( Q ) = Q 2 + 10 + 20 Q (b) For perfect competition, we have P ( Q ) = MC ( Q ) 100- Q = Q + 10 Q = 45 P = 100- 45 = 55 Profit is then defined as π ( Q ) = TR ( Q )- TC ( Q ) = 100 Q- Q 2- Q 2 2- 10 Q- 20 = 90 Q- 3 2 Q 2- 20 = 992 . 5 (c) For monopolist, we have MR ( Q ) = MC ( Q ) 100- 2 Q = Q + 10 Q = 30 P = 100- 30 = 70 Profit is then π ( Q ) = 90 Q- 3 2 Q 2- 20 = 1330 . 2. (a) The monopolist problem is maximizing profit, which is total revenue minus total cost....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

HW4solution - Micro 3101 Solution to Homework Assignment 4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online