April 25, 2015

Homework Help: ECON

Posted by Trisha on Friday, June 24, 2005 at 1:03pm.

I am working on this but, if I have part a and b wrong, all of the following question related will be wrong. Can you help me out?

The market for product A has the following functions:

Market demand Q=1,000-4P
Market supply Q=1/2P
Inverse market demand P=250-.25Q
Marginal Revenue MR=250-.5Q
Total Cost TC=Q(squared)
Marginal Cost MC=2Q

a) Assuming product A is produced in a perfectly competitive market, compute the market's producer and consumer surplus.

b)Assuming product A is produced in a monopolistically ompetitive market, compute the firm's short-run maximum profit or loss.


For a) i get P=222.2, Q=111.11. Total consumer surplus is the area of the triangle above price and below demand = .5*(250-222.2)*111.11 = 1544.4. Total producer surplus is the area of the triangle below price and above supply = .5*222.2*111.11=12344.3

For b) i get P = 225, Q=100. (you take if from here)

I don't understand how the p=222.2 is calculated. I know where it is on the graph, but how do you get it? I thought it was MR=MC but that would be 100. Can you explain it?

Ok, in the competitive market, equilibrium is when supply=demand. From your equations, 1000-4P = 1/2P.
Solve for P. (I get 222.2).

For the monopolist, set MR=MC, and as you say, Q=100. From the demand curve, when Q=100 then P=225.

Oh, Okay. Thanks!

Referring back to problem b. It looks to me like Firm A has a short run max. profit rather than a loss. Right?

Right. You can calculate total profit as TR-TC (at price P and quantity Q).

TR=P*Q, and TC=Q^2.

same same. ATC is average total cost, which is TC/Q. Substitute this in for ATC and your get profit= (P - TC/Q)Q = PQ-TC. Since P*Q is total revenue, profit = TR-TC, which makes sense; profit is total revenues less total costs.


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