Question

Imagine you are given a TC function, a MC function, and a price P for a competitive firm.

1. Describe the steps that you would take to find the quantity Q that that firm will produce, and the profit it will make.

2. Draw a graph following the steps you’ve written in the previous question. Graph P, MC, and AC, and mark Q and profit. Draw the graph such that the firm makes a positive profit.

Answer 1

.1 Given are the total cost function, marginal cost function and price P for the firm. For a PC firm, the given P=MR=AR. Hence the firm faces a horizontal price function. Finally the output condition will be given where MR=MC. Let's enlist the steps as follows -

i. We write TR function by doing a P×Q and then find the MR by doing a dTR/dQ which will be equal to P.

ii. Now we can simply equate the P=MR with the MC and find the output at this level. This will give us the equilibrium quantity.

iii. Now we can find the profits by finding the difference between TC and TR at equilibrium output. TC can be given as AC × Q. While TR is P×Q.

2. In the graph we draw the P=MR=AR as a horizontal straight line. The AC curve is U shaped in nature while the MC is upward rising. The point where MR and MC intersect is the profit maximizing point for the PC firm. The profit is given by the rectangular area between AC at Q and P at Q. Since profits are positive P>AC.

In the diagram equilibrium occurs at e where P=MC. At this level output is Q and the profits equal area of rectangle ACeceP. This area is shaded in the diagram.