Posted by **Brett** on Tuesday, October 16, 2007 at 9:44pm.

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

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

thank you

- MICROECONOMICS -
**economyst**, Wednesday, October 17, 2007 at 4:57pm
always always always, MC=MR.

First rearrange the demand function to be P=f(Q). That is P=33.33 - Q/3

Now then Total revenue is P*Q. So TR=33.33Q -(Q^2)/3

MR is the first derivitive of TR. So MR=33.33 - (2/3)Q

MC is the first derivitive of TC. So MC=(1/2)Q

MC=MR - use algebra and solve for Q. Take it from here

- MICROECONOMICS -
**economyst**, Wednesday, October 17, 2007 at 5:03pm
oops, my bad algebra. I divided by 3 instead of multiplying by 3. So, P should be P=300 - 3Q.

But follow the same methodology as before starting from here.

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