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: $$\begin{aligned}\text { Demand: } P &=70-Q \\\text { Marginal Revenue: } M R &=70-2 Q \\\text { Marginal cost: } M C &=10+Q\end{aligned}$$ a. Graph these three curves. Assuming that $\mathrm{Mr}$. 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 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 So we have henry potter in as well, and the first thing we have to do is draw ourselves a graph.

00:04 So the formatting is a little weird, so i hope this is right, because it's hard to read the question properly.

00:13 But i think demand is equal to 70 minus q, i'm pretty sure.

00:19 Yeah.

00:20 Okay, so we start at 70, and this is going to be kind of a rough sketch.

00:27 I would recommend you try to do a better one if you can, because i'm, don't have like grid marks or anything here.

00:37 Demand.

00:38 Okay, that is quantity demanded.

00:43 And then marginal revenue is 70 minus 2q.

00:52 70 minus 2q.

00:55 So we got the same starting point, and i'm just going to figure out the final, let's see.

01:12 Basically all i did here was set quantity i mean sorry price equal to zero to figure out to figure out basically where this will be and i realized i kind of wrote these wrong so let me fix this up okay so this is demand p equals pretty sure that's the formatting issue there okay this is marginal revenue and this is marginal cost and marginal cost is 10 plus q equals p.

01:53 Okay.

01:55 So let's draw that one.

01:56 We've got 10 down here.

01:59 And since this seems to just go up to 70, let's just do that.

02:03 So we plug in 70 for q, and we get that the price here will be 80.

02:14 So this graph will look like that.

02:17 Okay.

02:19 So assuming that he maximizes profit, what quantity does he produce? one thing that we should also note is that he owns the only well in town with clean drinking water, which means this is a monopoly.

02:36 So that means that mr.

02:38 Potter can basically, this is the equilibrium here, but he's going to charge around there.

02:48 So to figure this out, i realize that my graph is kind of bad.

02:53 So what we got to do here is set marginal revenue and the marginal cost curve equal to each other.

03:03 The sony minus 2q equal to 10 plus q.

03:06 And the reason i'm doing this is because that's the intersection point.

03:10 That would be the equilibrium.

03:12 If this was a comp, yeah, it is the equilibrium.

03:15 But since this is a monopoly, we know that he's going to charge a markup price.

03:19 So we got to figure out what this quantity is so we can figure that out.

03:22 So we subtract 10 from both sides, just some algebra here, and we add to q over, and we get that 60 equals 3q, so that quantity is 20.

03:40 And if we plug that into either one of these equations, let's plug it into the 10 plus q.

03:47 Then if that's 20, then that is going to equal 30.

03:51 So we know that this is 30.

03:52 Okay, so now that we have that, we know that the quantity is 20, we can plug that into the demand curve because remember, that's how monopolists set their price.

04:03 So we know this is 50.

04:05 So for part a, the price that he sets, and the quantity, the quantity is 20 gallons or something, and the price is, what did i say, 50? okay, next part.

04:23 So, mayor bailey wants to consider a price ceiling 10 % below the monopoly price.

04:34 So, what quantity would that be? so 10 % below means, okay, 10 % below equilibrium means 0 .90 times 50, right? because we're just finding 10 % less.

04:52 So 0 .9 times 50 is $45.

04:58 So mr.

04:59 Bailey would like to drop this price down to 45.

05:05 Again, the way i did that 10 % below 0 .9 times 50.

05:09 Okay, so what quantity would be demanded at this new price? if, if, okay, so if we set 45, which is our price, equal to the quantity, because we want to solve for the quantity, quantity, right? so 45, because remember monopoulos set their price by the demand curve equals 70 minus q.

05:41 You know that q is going to be, i can do math, 25.

05:48 And if we look at 25 here, it would be somewhere like here, right? that means that's the quantity that mr...

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