Question

Henry Potter owns the only well in town that produces clean drinking water. He faces the following demand, marginal-revenue, and marginal-cost cruves: Demand: P=70−QMarginal 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. Mayer George Bailey, concerned about water consumers, is considering a price ceiling 10% below the monopoly price derived in a. What quantity would be demanded at this new price? Would the profit-maximizing Mr. Potter produce that amount? Explain. 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%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? ( 20 marks)

Answer 1

Answer and Explanation:

a. To graph the demand, marginal revenue, and marginal cost curves, we will use the given equations:

Demand: P = 70 - Q

Marginal Revenue: MR = 70 - 2Q

Marginal Cost: MC = 10 + Q

On a graph, the quantity (Q) will be on the x-axis, and the price (P) will be on the y-axis.

To find the profit-maximizing quantity, we need to find the quantity where marginal revenue equals marginal cost.

Setting MR equal to MC:

70 - 2Q = 10 + Q

Simplifying the equation:

3Q = 60

Q = 20

So, Mr. Potter will produce 20 units of water.

To find the price he charges, we can substitute the quantity into the demand equation:

P = 70 - Q

P = 70 - 20

P = 50

Therefore, Mr. Potter will charge a price of £50 per unit.

b. If a price ceiling is set 10% below the monopoly price derived in part a, the new price would be 90% of £50, which is £45.

To find the quantity demanded at this new price, we can substitute the price into the demand equation:

P = 70 - Q

£45 = 70 - Q

Q = 70 - £45

Q = 25

The quantity demanded at this new price would be 25 units. However, the profit-maximizing Mr. Potter would still produce 20 units (as determined in part a) because his marginal cost is lower than the price ceiling. This means there would be a shortage of 5 units (25 demanded - 20 produced).

c. Uncle Billy is correct that price ceilings can cause shortages. In this case, a price ceiling 10% below the monopoly price would create a shortage of 5 units (as determined in part b).

d. If a price ceiling is set 50% below the monopoly price derived in part a, the new price would be 50% of £50, which is £25.

To find the quantity demanded at this new price, we can substitute the price into the demand equation:

P = 70 - Q

£25 = 70 - Q

Q = 70 - £25

Q = 45

At this price, the quantity demanded would be 45 units. However, Mr. Potter would still produce 20 units (as determined in part a) because his marginal cost is lower than the price ceiling. This means there would be a shortage of 25 units (45 demanded - 20 produced).

In conclusion, price ceilings can result in shortages when the price ceiling is set below the equilibrium price determined by the intersection of marginal revenue and marginal cost. The size of the shortage depends on the difference between the quantity demanded at the price ceiling and the quantity produced.