# Economics

posted by .

Suppose a firm faces a downward sloping demand curve givven by the equation 1=100-1/3P. The firm's cost function is given by the equation C=30+1/4Q^2. Find the profit maximizing level of output.

• Economics -

always always always, MC=MR.

First rearrange the demand function to be P=f(Q). That is P=300 - 3Q
Now then Total revenue is P*Q. So TR=300Q -3(Q^2)
MR is the first derivitive of TR. So MR=300 - 6Q
MC is the first derivitive of TC. So MC=(1/2)Q
MC=MR - use algebra and solve for Q. Take it from here

## Similar Questions

1. ### MICROECONOMICS

Hello ive been struggling with this problem for about 2 days now could someone walk me through it?
2. ### Economics

A firm with monoply power has the demand curve: P = 100 - 3Q + 4A^1/2 And has the total cost function: C = 4Q^2 + 10Q + A where A is the level of advertising expenditures. P is price, Q is output. How do I find the values of A, Q, …
3. ### managerial economics

A firm uses a single plant with costs C= 160 +16Q +.1Q2 and faces the price equation P= 96 – .4Q. a) Find the firm’s profit-maximizing price and quantity. What is the profit?
4. ### ECONOMICS

A firm uses a single plant with costs C= 160 +16Q +.1Q2 and faces the price equation P= 96 – .4Q. a) Find the firm’s profit-maximizing price and quantity. What is the profit?
5. ### Economics

Suppose a monopolistically competitive firm’s demand is given by P = 100 – 2Q And its cost function is given by TC = 5 + 2Q a. Find the profit maximizing quantity, price, and total profit level. b. Is this a long-run or a short-run …
6. ### Economics

A firm uses a single plant with costs C = 160 + 16Q + .1Q2 and faces the price equation P = 96 - .4Q. a. Find the firm’s profit-maximizing price and quantity. What is its profit?
7. ### economics

A monopoly firm is faced with the following demand function P = 13 – 0.5Q The Marginal Cost function for the firm is given by 3 + 4Q and the total fixed cost is 4 Determine 1. The the profit maximizing output 2.The level of supernormal …
8. ### Microeconomics

A monopoly firm is faced with the following demand function P = 26 – 0.5Q. The Marginal Cost function for the firm is given by 6 + 6Q and the total fixed cost is 4. Determine a) The profit maximizing output. b) The level of supernormal …
9. ### Microeconomics

A monopoly firm is faced with the following demand function P = 26 – 0.5Q. The Marginal Cost function for the firm is given by 6 + 6Q and the total fixed cost is 4. Determine a) The profit maximizing output. b) The level of supernormal …
10. ### Economics

A monopoly firm faces a demand curve given by the following equation: P = \$500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = \$100 per day. Assume that the firm faces no fixed cost. You may wish …

More Similar Questions