Answer to Question #275363 in Microeconomics for khashayar

Question

4. 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.

Answer 1

a) Profit is maximized at;

$MR=MC$

$70-2Q=10+Q$

$Q=\frac{60}{3}=20$

$P=70-Q=70-20=50$

$10\%$ below monopoly price$=50(0.9)=45$

$D=70-Q=70-45=25$

$MC=10+25=35,$ MC is less than price

Supply -demand is $35-25=10$ (surplus)

At $P=$ $50\%$ below monopoly price; Q=70-25=45

25=10+Q

Q=15(supply)

There is a shortage of 45-15=30

(b)

Now, Mayor George Bailey, concerned about water consumers, is considering a price ceiling that is of $10\%$ below the monopoly price. 

Then, the price ceiling would be equal to$(50- 5) = \$ 45$ .

And at that price of $\$45$ , quantity demanded would be 25 units of output.

No, the profit maximizing Mr. potter would not produce that amount because quantity supplied is more than quantity demanded.

 

(c)

Now, George's uncle Billy says that a price ceiling is a bad idea because price ceiling cause shortages. Yes, he is right in this case. 

Because we can see from the above figure that price ceiling cause shortages. Size of shortage that price ceiling creates = [Quantity supplied at $\$45$ - Quantity demanded at] = [$\$45$ 35 - 25] = 10 units of output.

The shortage is because of lack of demand.