Question

Reconsider the common resource problem given in Example 18.6. Suppose that crawfish popularity continues to increase, and that the demand curve shifts from

C = 0.401 - 0.0064F to C = 0.50 - 0.0064F. How Does this shift in demand affect the actual crawfish catch, the efficient catch, and the social cost of common access? (Hint: Use the marginal social cost and private cost curves given in the example.)

Short answer

With an increase in the demand curve, that is, a shift along the demand curve, the actual crawfish catch will increase, which will deteriorate the efficiency level, increasing the social cost of common access.

Step-by-step solution

The efficient number of public televisions

From example 18.6, information regarding the marginal social cost and the marginal private cost is given. Given the new demand curve,

Demand; $C=0.50-0.0064F$

MSC; $C=-5.645+0.6509F$

MPC; $C=-0.357+0.0573F$

With an increase in demand, the demand curve for crawfish shifts upward at demand’, intersecting the cost curves and establishing a price at $0.50. Since both the private cost curve and the social cost curve have a positive slope.

Therefore, an additional effort must be made to increase the catch. Thus, the socially efficient catch will increase.

Now to determine the socially efficient catch, set demand equal to MSC:

$$\begin{gathered} \text{MSB = MSC} \\ \text{0.50 - 0.0064F = - 5.645 + 0.6509F} \\ \text{F = 9.35} \end{gathered}$$

Now to determine the price consumers are willing to pay for this quantity, substitute Fin the demand equation:

$$\begin{gathered} \text{C = 0.50 - 0.0064}\left(\text{9.35}\right) \\ \text{C = \$ 0.44} \end{gathered}$$

Now to know the actual crawfish catch, equate the demand and private marginal cost:

$$\begin{gathered} \text{MSB = MPC} \\ \text{0.50 - 0.0064F = - 0.357 + 0.0573F} \\ \text{F* = 13.45} \end{gathered}$$

To find out the price consumers are willing to pay at the above, substitute 13.45 or F*in the demand equation:

$$\begin{gathered} \text{C = 0.50 - 0.0064}\left(\text{9.35}\right) \\ \text{C = \$ 0.41} \end{gathered}$$

Notice that the MSC of producing 13.45 units will:

$$\begin{gathered} \text{MSC = - 5.645 + 0.6509}\left(\text{13.45}\right) \\ \text{MSC = \$ 3.1} \end{gathered}$$

Therefore, with an increase in demand at 0.50, the marginal social cost of common access will be;

9.35-13.45= 4.1(difference between the social efficient catch and actual catch)

3.11- 0.41= 2.70 (difference between willingness to pay for the social efficient catch and willingness to pay for the actual catch)

$0.5\times 4.1\times 2.70=5.535$

This is greater than the MSC given in the example; that is, 2,396.