Question

Reconsider the common resource problem given in Example \(18.7 .\) Suppose that crawfish popularity continues to increase, and that the demand curve shifts from \(C=0.401-0.0064 F\) to \(C=0.50-0.0064 F\) 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

This shift in demand leads to an increase in both the actual and efficient crawfish catch, due to higher willingness to pay. However, it also generates a larger social cost due to overconsumption.

Step-by-step solution

Understanding the initial demand price function and quantity function

The initial demand function for crawfish was \(C=0.401-0.0064F\), where C is the price of crawfish and F is the number of crawfish caught.

Understanding the new demand function

Due to an increase in popularity, the demand curve shifts upwards to \(C=0.50-0.0064F\). This suggests that the price people are willing to pay for crawfish has increased, while the quantity demanded decreases with F.

Calculating changes in crawfish catch

To find the actual catch, this will be where the new demand equals to the private cost. Equate both equations given in the example and solve for F.

Efficient Catch Calculation

The efficient catch is where demand equals to the social cost. Equate the given social cost equation to the new demand equation and solve for F.

Impact on the social cost

The social cost can be found by comparing the actual catch and the efficient catch. The increased demand curve means people are willing to pay more for the same quantity, implying an increased consumption which leads to an increase in social cost.

Key concepts

Demand Curve Shift

A demand curve shift occurs when there is a change in how much of a product consumers want at every price level. In this scenario, the demand curve for crawfish shifted upward due to increased popularity. Originally, the demand was represented by the function \(C=0.401-0.0064F\). This equation shows the relationship between price \(C\) and quantity \(F\) of crawfish. The new demand function \(C=0.50-0.0064F\) indicates a higher price consumers are willing to pay.
This shift means that even if the quantity remains the same, the price consumers are prepared to pay has increased, reflecting greater demand. Key implications include:

• An increased price at each quantity level
• A higher intersection point with other economic curves

This change affects both the actual and efficient level of crawfish catch as well.

Marginal Social Cost

Marginal social cost (MSC) is the total cost to society of producing an additional unit of a good. This includes both private costs and any external costs. When the demand curve for crawfish shifts, it affects the MSC because the increased catch due to higher consumer willingness to pay leads to more resources being used.
The MSC can be represented by a curve that shows the relationship between the cost of catching additional crawfish and the quantity caught. As demand increases, this curve may shift or steepen, indicating that the cost to society of catching each additional crawfish has increased. This concept helps determine the efficient catch point by balancing societal costs with demand.

Private Cost

Private cost refers to the expense incurred directly by the producers of a good or service. In our case, it pertains to those catching the crawfish. Unlike marginal social cost, private costs do not include externalities. When the demand curve shifts, it impacts the equilibrium point where the demand and private cost curves intersect.
The intersection determines the actual number of crawfish caught, which is driven by the market's supply and demand balance. Understanding this helps in analyzing how changes in consumer interest affect the producers directly and influence market decisions.
Knowing private costs is essential for businesses to set prices effectively and for policymakers to understand how private interests align with or differ from public interests.

Efficient Catch

Efficient catch is achieved when the quantity of a common resource, like crawfish, caught matches the quantity where marginal social benefits equal marginal social costs. This is optimal as it reflects a balance where resources are allocated without excessive overuse or waste.
When the demand curve shifts, the efficient catch point changes as well. In this instance, it requires balancing the new, higher consumer demand with the cost of potential overuse, which could deplete the crawfish stock.

• Ensures sustainability
• Aligns usage with societal well-being

Calculating the efficient catch involves equating the new demand to marginal social costs, which requires understanding both these factors' equations.
This involves analysis to find where the new demand curve intersects with the marginal social cost curve, which results in efficient use of the resource.