Henry Potter owns the only well in town that produces clean...

Henry Potter owns the only well in town that produces clean drinking water. He faces the following demand, marginal revenue, and marginal cost curves: Demand: $P = 70 - Q$ Marginal Revenue: $MR = 70 - 2Q$ Marginal Cost: $MC = 10 + Q$ a. Graph these three curves. Assuming that Mr. Potter maximizes profit, what quantity does he produce? What price does he charge? Show these results on your graph. b. Mayor George Bailey, concerned about water consumers, is considering a price ceiling that is 10 percent below the monopoly price derived in part (a). What quantity would be demanded at this new price? Would the profit-maximizing Mr. Potter produce that amount? Explain. ($Hint$: Think about marginal cost.) c. George's Uncle Billy says that a price ceiling is a bad idea because price ceilings cause shortages. Is he right in this case? What size shortage would the price ceiling create? Explain. d. George's friend Clarence, who is even more concerned about consumers, suggests a price ceiling 50 percent below the monopoly price. What quantity would be demanded at this price? How much would Mr. Potter produce? In this case, is Uncle Billy right? What size shortage would the price ceiling create?

Henry Potter owns the only well in town that produces clean drinking water. He faces the following
demand, marginal revenue, and marginal cost curves: Demand: $P = 70 - Q$ Marginal Revenue: $MR = 70 - 2Q$ Marginal Cost: $MC = 10 + Q$
a. Graph these three curves. Assuming that Mr. Potter maximizes profit, what quantity does he produce? What price does he charge? Show these results on your graph.
b. Mayor George Bailey, concerned about water consumers, is considering a price ceiling that is 10 percent below the monopoly price derived in part (a). What quantity would be demanded at this new price? Would the profit-maximizing Mr. Potter produce that amount? Explain. ($Hint$: Think about marginal cost.)
c. George's Uncle Billy says that a price ceiling is a bad idea because price ceilings cause shortages. Is he right in this case? What size shortage would the price ceiling create? Explain.
d. George's friend Clarence, who is even more concerned about consumers, suggests a price ceiling
50 percent below the monopoly price. What quantity would be demanded at this price? How much
would Mr. Potter produce? In this case, is Uncle Billy right? What size shortage would the price ceiling create?

Transcript

00:01 Okay, guys, this is chapter 15 problem.

00:04 Eight on this problem were given that the demand occur is given by this equation.

00:10 Pain equals 70 minus.

00:12 Q.

00:13 Marginal cost is given by 10 plus q and marginal.

00:17 Every revenue is given by 70 minus two.

00:20 Q.

00:21 So for the first part, we're told to grab the curves.

00:24 And then if mr potter, who owns this well that we're using, is good in this problem, he's maximizing profits.

00:33 Then how much will he produce? and so anybody who's maximizing profits is going to produce were marginal cost people's marginal revenue.

00:43 And so, in this case, we just then set the marginal constant marginal revenue curves together 10 plus q equals 70 minus two q.

00:53 Right, and we get three.

00:55 Q equals 60 and q equals 20 and then put this back into the demand current of cubicles 20 and people 70 minus.

01:05 Q.

01:06 P equals 70 minus 20 and peoples 50 spencer than we can grant fat.

01:13 It's me price, billy of quantity.

01:17 And so we started here, with prices equal the 70 and price minus to you down here, then this is also going to be 70 for the demand cur we have.

01:28 This marginal remini curve is 70 minus two q.

01:35 So this is going to be 35.

01:37 This is a marginal revenue, and then marginal con starts here a 10 and gives out with you.

01:50 But the second part of this question, we were asked if there's now a 10% price feeling how much would be demanded and how much will mr parr and would mr pond and produced this? and so if we saw the equilibrium price was 50 so 10 per cent of 50 is five.

02:09 And so the new price with the price ceiling so price some c for stealing is going to equal 45 about how much people demand.

02:18 Then we plug that back in to the demand curve from p equals 70 minus was dying 70 minus q.

02:28 And so p is now set to equal 45.

02:31 Equal 70 minus.

02:32 Q.

02:33 And then q is going teo equal 25.

02:39 Uh, if mr potter is coffin maximising, remember from the graph that the equilibrium was here cubicles 20 and acid.

02:50 Here's marginal revenue, and here's marginal cost over here...