Chapter 17, Problem 5P

 (a)

To determine

The private demand and marginal cost (MC) curves.

Explanation of Solution

Figure 1 illustrates the private demand curve and the MC curve.

In Figure 1, the vertical axis measures the price of drive-in movies and the horizontal axis measures the quantity of drive-in movies, where curve D shows the private demand function $\text{P}=20-0.1\text{Q}$, and the MC curve shows the MC of showing drive-in movies, which is $\text{MC}=0.1\text{Q}$. The equilibrium price and equilibrium quantity is determined at the point where the demand curve equals to the MC curve.

Now set the two expressions to get the value of quantity.

$\begin{array}{c}20-0.1\text{Q}=0.1\text{Q}\\ 20=0.2\text{Q}\\ \text{Q}=\frac{20}{0.2}\\ =100\end{array}$

Therefore, the quantity of drive-in movies is 100.

Substitute the respective value into the demand function to get the value of price.

$\begin{array}{c}\text{P}=20-0.1\times 100\\ =20-10\\ =10\end{array}$

Therefore, the price of drive-in movies is 10.

Economics Concept Introduction

Marginal cost (MC): The marginal cost refers to the amount of an additional cost incurred in the process of increasing one more unit of output.

 (b)

To determine

The external marginal benefit (EMB) curve.

Explanation of Solution

The figure 2 illustrates the EMB curve and the social demand curve. 

In the figure 2, the vertical axis measures the price of movies and the horizontal axis measures the quantity of drive-in movies where the curve D shows the demand function $\text{P}=20-0.1\text{Q}$, and the MC curve shows the MC of showing drive-in movies which is $\text{MC}=0.1\text{Q}$ and EMB curve function is $\text{EMB}=2-0.01\text{Q}$  where the social demand (SD) curve is the sum total of demand function and the EMB.

$\begin{array}{c}\text{SD}=\text{D}+\text{EMB}\\ 20-0.1\text{Q}+2-0.01\text{Q}\\ =22-0.11\text{Q}\end{array}$

Therefore, the social demand function is $\text{SD}=22-0.11\text{Q}$.

Economics Concept Introduction

External marginal benefit: The EMB is the benefit conferred on a third party when an additional unit of a good is produced or consumed.

 (c)

To determine

The optimal price and quantity of drive-in movies.

Explanation of Solution

The optimal price and optimal quantity is determined at the point where the social demand curve equals to the MC curve.

Now set the two expressions to get the value of optimal quantity.

$\begin{array}{c}22-0.11\text{Q}=0.1\text{Q}\\ 22=0.21\text{Q}\\ \text{Q}=\frac{22}{0.21}\\ =105\end{array}$

Therefore, the optimal quantity of drive-in movies is around 105.

Substitute the respective value into the social demand function to get the value of optimal price.

$\begin{array}{c}\text{P}=22-\left(0.11\times 105\right)\\ =22-11.55\\ =\$10.45\end{array}$

Therefore, the optimal price of drive-in movies is $10.45.

Economics Concept Introduction

Marginal cost (MC): The marginal cost refers to the amount of an additional cost incurred in the process of increasing one more unit of output.

 (d)

To determine

The dead weight loss.

Explanation of Solution

The dead weight loss is the inefficient level of production in an economy. It can calculated by using the following formula.

$\begin{array}{c}\text{Dead weight loss}=\frac{1}{2}\times \left(\begin{array}{l}\text{Maximum willing to offer}\\ \text{ price}-\text{Actually }\\ \text{paying price}\end{array}\right)\times \left(\begin{array}{l}\text{Maximum Quantity}-\\ \text{Actual quantity}\end{array}\right)\\ \end{array}$ (1)

Here, the actually paying price can calculated by substituting the new optimal quantity into the private demand function.

$\begin{array}{c}\text{Actual price}=20-\left(0.1\times 105\right)\\ =20-10.5\\ =\$9.50\end{array}$

Therefore, the actual price is $9.50.

Now substitute the respective values into the equation (1) for solve the dead weight loss.

$\begin{array}{c}\text{Deadweight loss}=\frac{1}{2}\times \left(10.45-9.50\right)\times \left(105-100\right)\\ =\$2.375\end{array}$

Therefore, the dead weight loss is $2.375.

Economics Concept Introduction

Dead weight loss: Dead weight loss is the decreases in the total surplus in an economy due to an inefficient level of production.

 (e)

To determine

The effect of positive market externality on outcome.

Explanation of Solution

The positive externality is a benefit conferred on a third party not directly involved in an economic transaction. In this case, the presence of positive externality in the theatre business helps the government to increase the output up to a socially optimal level. The government can also achieve this socially optimal level of output through a price-based intervention called subsidy. Hence, the government run movies can potentially improve on the private market outcome.

Economics Concept Introduction

Positive externality: The positive externality is a benefit conferred on third parties who are not directly involved in an economic transaction.