Calculate the firm's profit and producer surplus at the equilibrium level of output.?

Question

Information given:

TC = 200 + 2q² , where TC is the Total Cost, and q is the output.

Help here would be much appreciated.

Answer 1

Very interesting question you had.

The keyword is 'equilibrium'

This is what I have, I don't know how far had I got it:

TC = 200+2q^2

MC = 4q

at eqm, MC = MR = 4q

TR = Pq

MR = dTR/dq = P = 4q

Profit = TR - TC

          = Pq - (200+2q^2)

          = 4q(q) - 200 - 2q^2

          = 2q^2 - 200

I'm stuck at here. Actually was wondering, is the market structure monopoly, oligopoly, PC or monopolistic comp?

Ok, if it is PC, then it's easy, simply set profit = 0

From there, we can derive the quantity:

2q^2 - 200 = 0

2q^2 = 200

q^2 = 100

q = 10

When q = 10

P = 4q = 40

MC = 4q

When q = 0 (to find the vertical axis intercept),

MC = 0; We can safely conclude that MC passes through the origin.

To find the producer surplus, simply find the area of the triangle below the equilibrium price:

0.5*40*10 = 200

I strongly suspect that this is a PC question. But anyway, hope the whole solution sounds logical to you ;) cheers

Since they're not asking for consumer surplus, so you don't have to worry about the demand function. :p

Answer 2

Given task can't be calculated with these details.

Supply curve is derived from TC curve. Supply curve is marginal cost curve above ATC or above AVC - depending of long or short-runs.

So you can calculate producer surplus (profit), it's difference between MC and ATC curve multiplied by quantity.

ATC=TC/Q

MC=(TC)'

ATC=200/Q+2Q

MC=4Q

Profit=(4Q-200/Q-2Q)*Q=2Q²-200

Minimal price required for zero economic profit is at quantity ATC=MC

200/Q+2Q=4Q

200/Q=2Q

Q=10

TC(10)=200+200=400

400/10=40

P(min)=40 Q(min)=10 Above this point (including) firm will have surplus (2Q²-200).

To calculate consumer surplus you need to know utility or demand functions.