Chapter 11, Problem 11.10P

a)

To determine

The industry outcome under unregulated monopoly is to be calculated.

Answer to Problem 11.10P

The price is $60 and the quantity is 40. The total revenue and total cost is $2,400 and $1,800 respectively. The profit earned is $600 and the consumer surplus is $800

Explanation of Solution

The natural gas is a natural monopoly and the demand curve is given in the question as $Q=100-P$ . The marginal t=revenue curve is $MR=100-2Q$ . The total cost is given by $TC=1000+20Q$ and the marginal cost by $MC=20$ .

According to the given condition,

  $\begin{array}{l}\text{Marginal revenue(MR) = Marginal cost(MC)}\\ 100-2Q=20\\ 2Q=80\\ Q=40\\ 40+100-P\\ P=60\end{array}$

The price per unit is $60 and the quantity is 40.

Substitute the values in

  $\begin{array}{l}\text{Total revenue = Price × Quantity}\\ TR=PQ\\ TR=\$60(40)=\$2,400\\ TC=\$1,000+\$20(40)=\$1,800\end{array}$

Total revenue earned is$2,400 and the total cost incurred is $1,800.

Profit earned can be calculated as

  $\begin{array}{l}\pi =\text{Total revenue - Total cost}\\ \pi =TR-TC=2,400-1,800=600\end{array}$

The graph of the given unregulated monopoly can be drawn as:

  

Consumer surplus can be given by the area below the demand curve and above the price line,i.e. the triangle abc.

  $\begin{array}{l}\text{Area of triangle = }\frac{\text{1}}{\text{2}}\text{ × base × height}\\ \text{ = }\frac{1}{2}\times 40(100-6)=800\end{array}$

Total surplus is termed as the social welfare. Thus the value of social surplus in the given condition is $1,400 ($600+$800).

Economics Concept Introduction

Introduction: Monopoly is a market structure with a single firm selling a unique good. Monopoly is a price maker and has extensive market control. By analyzing the marginal revenue and marginal cost of producing an extra unit, a monopolist can determine its profit maximizing price and quantity.

b)

To determine

The regulatory price that maximizes social welfare and the industry outcome under this price is to be calculated.

Answer to Problem 11.10P

The price maximizes social welfare is $20 and the quantity sold will be 80 units. The profit earned will be -$1,000.

Explanation of Solution

The price for maximization of social welfare can be calculated as follows:

  $\begin{array}{l}P=MC\\ 100-Q=20\\ Q=80\end{array}$

By substitution,

  $\begin{array}{l}\text{Total revenue = Price × Quantity}\\ TR=PQ\\ TR=\$20(80)=\$1,600\\ TC=\$1,000+\$20(80)=\$2,600\end{array}$

Profit is calculated by

  $\begin{array}{l}\pi =\text{Total revenue - Total cost}\\ \pi =TR-TC=1,600-2,600=-\$1,000\end{array}$

This indicates that the regulated monopoly has a negative profit which means loss.

Consumer surplus can be given by the area below the demand curve and above the price line, i.e. the triangle ade.

  $\begin{array}{l}\text{Area of triangle = }\frac{\text{1}}{\text{2}}\text{ × base × height}\\ \text{ = }\frac{1}{2}\times (80-0)(100-20)=3,200\end{array}$

The value of social surplus under regulated monopoly is $2,200 ($3,200-$1,000). The policy of regulation is not sustainable even though it maximizes the social welfare, but it makes the firm losses.

Economics Concept Introduction

Introduction: Monopoly is a market structure with a single firm selling a unique good. Monopoly is a price maker and has extensive market control. By analyzing the marginal revenue and marginal cost of producing an extra unit, a monopolist can determine its profit maximizing price and quantity.

c)

To determine

The industry outcome with the laxer regulatory policy of constraining price and the sustainability of the policy in a long run is to be determined.

Answer to Problem 11.10P

The optimal quantity produced in the given case is 64.5 units.

Explanation of Solution

According to the given condition, price and average cost of production will be charged equal.

  $\begin{array}{l}C=1000+20Q\\ AC=\frac{C}{Q}=\frac{1000}{Q}+20\\ \text{Substitute P}\\ P=\frac{1000}{Q}+20\\ \frac{1000}{Q}+20=100-Q\\ \frac{1000}{Q}+Q=80\\ 1000+Q^2=80Q\\ Q^2-80Q+1000=0\\ \text{By solving the quadratic equation},\\ Q=\frac{-b\pm \sqrt{b^2}-4ac}{2a}\\ \text{ = }\frac{-(-80)\pm \sqrt{{(-80)}^2}-4(1)(1000)}{2(1)}\\ \text{ = }\frac{80\pm 48.98}{2}=\frac{128.98}{2},\frac{31.02}{2}\\ \text{ = }64.49,15.56\\ \end{array}$

The optimal quantity produced will be 64.5 units.

By substitution, we get the price per unit.

  $P=100-Q=100-64.5=\$35.5$

The profit in the given case should be zero as the price and the average production cost is charged equally.

Consumer surplus can be given by the area below the demand curve and above the price line, i.e. the triangle afg.

  $\begin{array}{l}\text{Area of triangle = }\frac{\text{1}}{\text{2}}\text{ × base × height}\\ \text{ = }\frac{1}{2}\times 64.5\times (100-35.5)=\$2,079.80\end{array}$

Therefore the consumer surplus is $2,079.80. The value of social welfare in this case is $2,079.80. The policy will be sustainable in long run as the firm is breaking even. This means that their profit is zero and has no incentive to exit.

Economics Concept Introduction

Introduction: Monopoly is a market structure with a single firm selling a unique good. Monopoly is a price maker and has extensive market control. By analyzing the marginal revenue and marginal cost of producing an extra unit, a monopolist can determine its profit maximizing price and quantity.