Ampstand is a natural monopolist earning economic profits.

(a) Draw a graph of Ampstand, labeling the profit-maximizing price Pm,  the profit-maximizing quantity Qm, and the allocatively efficient quantity QSO. Shade the area of deadweight loss.

(b) If Ampstand is earning economic profits, why would other firms not enter the market? Explain.

(c) The government decides to regulate Ampstand's price and follows a fair-return policy. On your graph from part (a), label this price PFR and the new output quantity QFR. 

(d) If Ampstand's total revenue at PFR changes to $100 million, what must its total cost be at this productive quantity? 

(e) Determine the output quantity from part (d) if PFR is $10. The demand curve intersects the y-axis at $15. What is the consumer surplus with the government intervention?

(f) How would the government action in part (c) affect the deadweight loss in Ampstand's market?

(g) What would the government have to do to get Ampstand to produce at the socially optimal quantity and stay in the market in the long run? Explain.

(h) Wattsit is a small firm that sells a complementary good to Ampstand's product in a perfectly competitive market. Assuming Wattsit was in long-run equilibrium, illustrate the short-run effect of the government intervention from part (e) on Wattsit's supply and demand in a separate graph. If Wattsit earns any economic profit or loss, shade it. 

(i) What happens to the demand for the inputs in the factor market required to produce Wattsit's good as a result of the changes in part (h)?

Answer:

a) The optimal quantity and price for a monopolist is the profit-maximizing one. This point is achieved where the MR(marginal revenue) and the MC(marginal cost) intersect. The price is determined by the demand curve. The efficient quantity is where the price is equated to the MC(marginal cost). The graph is drawn in the explanation section.

b) Other firms will not find it profitable to enter the market because the TFC(total fixed cost) in the case of a natural monopoly is very high. The market also faces economies of scale, thus new firms entering the market and producing a lower level of output would be at a loss.

c) The PFR will be at the level where Price=AC(Average Cost). The diagram is shown in the explanation below.

d) $100 million

e) Output=10 million, CS(Consumer Surplus)=$50 million

f) The deadweight loss will decrease as the quantity produced increases and the price charged decreases.

g) The government would have to provide a subsidy to compensate for the loss of the monopolist caused by selling at a price lower than the average cost.

h) The market demand curve for the complementary good's market will shift to the right. Thus, the price and quantity in the SR(short-run) equilibrium will increase. This increase in the market price would shift the price for the firm up, leading to economic profits.

i) The demand for the inputs will increase. This increase will shift the demand curve to the right causing an increase in the P(price) and Q(quantity) of the inputs in the market equilibrium.

Step-by-step explanation

a) A monopolist tries to maximize their own profit. This point is achieved where the MR=MC. In the diagram given below, the firm maximizes its long-run profits where MR=LRMC(Long Run Marginal Cost). At this point, the quantity produced is Qm. The price set by the monopolist is found corresponding to the profit-maximizing quantity on the demand curve, given by Pm.  This can be seen in Graph 1 shown below:

If the firm would have operated in a PC (perfectly competitive) market, the optimal price would be equal to the MC and the AR. Thus, the optimal price is given by PSO and the optimal quantity is given by QSO. The deadweight loss to the society is due to the higher price charged and a lower level of output being produced than socially optimum. This deadweight loss is shown in the diagram by the shaded area.

b) When the given firm is earning economic profits, new firms will not enter the market. This is because, in the case of a natural monopoly, the fixed costs are very large. A natural monopolist earns IRS(increasing returns to scale). This causes the LRAC to fall. The operation of only 1 firm can lead to a minimum efficient scale, which means if he/she produces the entire output for the economy. If any new firm enters the market, it would have to bear a large fixed cost and produce at a lower level of output due to the existence of a firm already in the market. This would cause the cost of production to be very large. Thus, no firm will want to enter the market.

c) If the government decides to regulate the natural monopolist, it will set the price at PFR and the quantity at QFR as shown below in Graph 2:

At this price level, the price=AC. The price is fair in the sense that it represents the AC(average cost) of production of the monopolist. The monopolist is still able to earn normal profits and at the same time, the price has reduced and the quantity produced has increased.

d) If the total revenue changes to $100 million, the total cost should also be equal to $100 million. This is because, at the fair-return price, the AC=PFR. It is given that TR=$100 million. Thus, 

The fair-return price is found by equating price to average cost:

Thus, the total costs will also be equal to $100 million.

e) The output quantity can be determined by using the total revenue given:

The PFR is given to be $10 and the TR is given as $100, thus the quantity will be:

Thus, the output quantity will be 10 million.

The consumer surplus is found by the difference between the price the consumer is WTP(willing to pay) and the price that is actually charged for the output being sold. Since the demand curve cuts the y-axis at $15, the maximum price the consumers are WTP(willing to pay) is $15 per unit while the price actually charged is $10. Thus, the consumer surplus is given by:

CS=(Maximum price willing to pay-Market Price) Quantity

CS=(15-10)10

CS=$50

Thus, the consumer surplus is $50 million

f) The deadweight loss of society gets reduced because the level of Q(output) being produced increases and the price being charged decreases. The deadweight loss is found by the formula:

Here, the difference in price refers to the difference between the monopoly price and the perfect competition price and the difference in quantity refers to the difference in the quantity sold by the monopolist and the quantity sold in a PC(perfectly competitive) market. The deadweight loss, therefore, exists because the monopolist produces a less than socially efficient level of Q(output) where all the resources of the economy are employed.

When the government regulates the monopoly such that the output level is increased, the deadweight loss decreases to ABC from DEC as shown in graph 2.

g) For the firm to produce at the socially optimal level, the government would have to compensate for the loss of the monopolist. This is because, at the socially optimal level QSO, the price-PSO is less than the AC of production given by Pa. This can be seen in graph 3 shown below:

The shaded region represents the loss of the firm if it charges PSO and produces QSO. The government can provide a subsidy of PaPSO per unit sold, in order to compensate for the loss of the monopolist.

h) As the output level increases for the monopolist, the demand for the complementary good also rises. This causes a shift in the price and quantity of the small competitive firm in the equilibrium producing the complementary good. It occurs as a result of the market demand curve shifting to the right as shown below in graph 4:

The shift in the demand curve leads to a rise in the price in the SR(short run), this increase in price causes the SR(short-run) equilibrium of the firm to shift as shown below in graph 5:

It is seen that the firm is earning an economic profit in the SR(short-run)represented by the shaded area. This profit is due to the price being more than the AC (average cost). The equilibrium price received by the firm in the SR(short-run) increases and the output being produced also increases.

i) As the demand for the complementary good increases, the producers find it profitable to produce more of the good. To increase the supply of goods, the suppliers need an increased amount of factors of production. This causes a rise in the demand for the inputs. This causes a rightward shift in the demand curve in the factor market as shown below in graph 6:

This rightward shift in the demand curve causes the equilibrium to shift upwards to the right. Thus, the equilibrium price and quantity of the factors of production increases.

Please find the attched file below:

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