1 50 total points suppose a monopolist faces the following...

1. (50 Total Points) Suppose a monopolist faces the following demand curve: P = 325 – 3Q. Also suppose the Marginal Cost of production for the monopolist is constant and equal to 25. So MC = 25. Also, the monopolist has no fixed costs. a) (6 points) How much output should the monopolist produce in order to maximize profit?

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00:01 So here we're talking monopoly and we have a demand curve, we have a marginal cost curve, and that's just 10.

00:08 Great.

00:09 So what i want to do for a monopoly is to set marginal revenue equals to marginal cost.

00:14 Now revenue is price times quantity.

00:17 Substitute in the demand curve to get a function just in terms of quantity.

00:22 Differentiate with respect to q to get the marginal revenue, which is 100 minus 6q.

00:27 Now set these things equal.

00:31 We get 6q is equal to 90, q is equal to 15.

00:36 Once you have q, you can get the price back in.

00:39 So the price would be equal to 100 minus 3 outside of 15, which is equal to 55.

00:46 So we've got the price and the quantity.

00:49 That's a and b.

00:51 The profit, so no fixed costs.

00:56 So for c, this is the profit is equal to price times quantity minus the marginal cost times the quantity, only because there are no fixed costs, right? which is equal to 55 times 15 minus 10 times 55.

01:16 I'm going to need a calculator for this one, but it's not too bad to get.

01:22 I get a profit of 675.

01:26 Now what i want to do for the other part is illustrate, because honestly, it's always a good idea to figure out what's going on.

01:36 So the demand curve starts here at 100 and slopes down pretty steep.

01:41 So this would be 33 .3...

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