# MICROECONOMICS

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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 -

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 -

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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