Ezekiel N. answered • 04/07/15
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This is a profit maximization question. The profit maximizing firm always sets marginal revenue equal to marginal cost, MR=MC. Also, for perfectly competitive firms P=MC, to get started we will take the firms total cost and solve for marginal cost, which will also give us the price that the firm is charging. Thus TC = 1500 + 200 Q + Q^2 and MC is equal to @TC/@Q or mathematically called the partial derivative of the total cost equation, we now have MC=@TC/@Q=200+2Q so the MC equation can now be expressed as MC=P=200+2Q, what we don't know is what the market price is, firms in perfect competition always take price as given so we now need to solve for the market price and we do that by setting Qs=Qd=Q which is 40,000 + 60 P = 80,000 – 40 P collecting terms and solving gives us 100p=40000, p=400. Substituting P=MC from above and evaluating we have 400=200+2(Q), Q=100 So the firm produces 100 units at a price of 400
2) What are the profits earned by the firm, remember that profit is always equal to total revenue minus total cost, Pr=TR-TC. We know what the total cost for the firm is, it was given as TC = 1500 + 200 Q + Q2, Using our results from above we solve for Total Revenue and also substitute Q=100 into the Total Cost equation. Now we have Pr=(100*400)-(1500+200(100)+(100^2) simplify. Pr=40000-31500, Pr=8500, the firm has economic profits of 8500.
3) If firms are making economic profits in a perfect competition the market is not in equilibrium. Because there are no barriers to entry if there are positive economic profits firms will enter the market as output increases price will fall and total quantity will rise until profits equal 0.
