Question

Hi, currently studying for an economics final where we have to figure out profit maximization when given a demand and cost function either in perfect competition market or monopolistic. I was wondering if anybody can throw some practice problems at me so that I can get some practice in for solving the profit maximization, MR, AR, MC, ATC, TR and such. So if possible, can you hit me with what you got and then include the problem worked out so that I can check my progress? Thank you!

Some examples I have been working on are Q=200-1/2P TC= 2+2Q2 which I have figured out but would like something similar.  

Answer 1

For profit maximization we have to solve MR = MC, so we will find profit maximizing quantity

Now we have to find profit maximizing price

In monopoly and monopolistic competition price is above MR, so to find price in monopoly/ monopolistic market, we have to put value of Q in demand function

In perfect competition MR = MC = AR, thus if you have demand function, convert it in TR function, derive MR from TR , equate, and put value of Q in MR to find equilibrium price as MR =Price in perfect competition

From TC we can derive MC

TC = 2 + 2Q^2

MC = 4Q

From demand function we have to make it TR function, TR = P * Q

Q = 200 - 1/2 P

1/2P = 200 - Q

P = 100 - Q/2

TR = P*Q

TR = 100Q - Q^2/2

MR is derivation of TR

MR = 100 - 4Q

MR = MC for profit max quantity

4Q = 100 - 4Q

8Q = 100

Q = 12.5

Suppose, the firm is in monopoly/monopolistic price will be find from demand function

Qd = 200 - 1/2P

12.5 = 200 - 1/2P

1/2P = 200 - 12.5

P = 375 is price of monopoly and monopolistic

Suppose firm is in perfect competition

MR = P

100 - 4Q = P

P = 100 - 4 (12.5)

P = 100 - 50

P = 50

We have price, TR, TC, MR, MC and quantity from this we can find AVC, ATC, AFC

More examples for practice

Example	demand function	total cost function
1	P = 107-2Q	TC = 200+3Q
2	P(Q) = 100 - 8Q	C(Q) = 50 + 80Q - 10Q^2 + 0.6Q^3
3	q = 1350 − 5p	C(q) = 60q + 4q^22