Question

Suppose Douglas and Ziffel have properties that adjoin the farm of Mr. Haney. The current zoning law permits Haney to use the farm for any purpose. Haney has decided to raise pigs (the best use of the land). A pig farm will earn \(\$ 50,000\) per year, forever. a. Assume the interest rate is 10 percent per year. What is Haney's pig farm worth? (Hint: Use a special formula from Chapter \(13 .)\) b. Suppose the next best use of Haney's property is residential, where it could earn \(\$ 20,000\) per year. What is the minimum one-time payment Haney would accept to agree to restrict his land for residential use forever? c. Suppose Douglas is willing to pay \(\$ 200,000\) for an end to pig farming on Haney's land, while Ziffel is willing to pay no more than \(\$ 150,000\) (For some reason, Ziffel does not mind pig farming as much as Douglas does.) If Douglas pays Haney \(\$ 200,000\) and Ziffel pays Haney \(\$ 150,000,\) and Haney converts his land to residential use, is this a Pareto improvement? Who benefits, who loses, and by how much? d. Suppose instead that Douglas pays \(\$ 150,000\) and Ziffel pays \(\$ 150,000 .\) Is this move a Pareto improvement? Who benefits, who loses, and by how much?

Short answer

a. The worth of the pig farm is calculated using the net present value formula, which yields \$500,000. b. The minimum one-time payment for residential use is the difference between this worth and the worth if the land was used for residential purposes, which is \$300,000. c. If Douglas and Ziffel's payments exceed this amount, this is a Pareto improvement, in which Haney benefits by the difference in payment and loss from conversion, and Douglas and Ziffel benefit by the difference between what they are willing to pay and the actual payment. d. The same goes for the second scenario, in which both Douglas and Ziffel pay \$150,000.

Step-by-step solution

Calculate the worth of Haney's pig farm

To find the worth of Haney's pig farm, we need to calculate the net present value (NPV) of the expected future cash flow, which is \$50,000 per year in perpetuity. The formula for NPV is \(NPV = CF/r\), where CF is the annual cash flow (here \$50,000) and r is the interest rate (here 0.10).

Determine the minimum payment for residential use

Because the land earning in residential use could be \$20,000 per year, the NPV is calculated the same way as in step 1, but with different cash flow. The minimum one-time payment that Haney would accept to convert his land to residential use would be the difference between the NPV of the pig farm and the NPV of the residential use.

Evaluate Pareto improvement in case 1

A Pareto improvement is a change which benefits at least one person without making anyone else worse off. If Douglas pays \$200,000 and Ziffel pays \$150,000 to prevent pig farming, and if the total of their payments is greater than Haney's loss from the conversion, then this is a Pareto improvement. The benefit or loss for each party is the difference of what they pay or receive and the NPV of their best alternative.

Evaluate Pareto improvement in case 2

In the second scenario where Douglas and Ziffel both pay \$150,000, we make a similar comparison to that in Step 3. If the total of their payments exceeds Haney's loss from the conversion, this is also a Pareto improvement. The benefit or loss for each party is determined in the same way as in step 3.

Key concepts

Net Present Value (NPV)

Net Present Value, often abbreviated as NPV, is a fundamental concept in microeconomics, used to determine the value of a stream of future cash flows. It helps in assessing the profitability of an investment or project.
To calculate NPV, you consider all the expected cash inflows and outflows of a project and discount them to the present moment using an appropriate interest rate.
This discounting process accounts for the time value of money, which suggests that money today is worth more than the same amount in the future. The formula for NPV is:

• \( NPV = \frac{CF}{r} \)
• where CF is the annual cash flow and r is the interest rate.

To fully understand the concept, imagine Haney's pig farm. It generates an annual cash flow of $50,000. Using the 10% interest rate provided, the NPV of this perpetual cash flow represents the worth of the pig farm. All these calculations help Haney decide whether maintaining the pig farm or switching to an alternative land use is more financially viable.

Pareto Improvement

In microeconomics, a Pareto improvement refers to a situation where making a change benefits at least one party without harming any others.
When considering changes in resource allocation or policy, achieving a Pareto improvement means no one is left worse off. In the context of Haney's land usage:

• Douglas and Ziffel wish to prevent pig farming, valuing non-farming at $200,000 and $150,000 respectively.
• If their combined payment to Haney is greater than the net present value loss Haney incurs by not farming pigs, then their decision to restrict pig use could be a Pareto improvement.

The idea is practical in determining whether economic agents (like Douglas, Ziffel, and Haney) can reach an agreement that leads to an overall better allocation of resources, without making anyone worse off than before.

Interest Rate

Interest rates play a crucial role in determining the net present value of future cash flows.
They represent the cost of capital and the relative risk of an investment.
In our exercise, the interest rate is set at 10%, a reasonable rate for discounting future cash inflows from Haney's pig farming. When calculating NPV, the interest rate helps convert the value of future cash earnings into present value. Understanding this rate is essential because it allows players like Haney to evaluate different scenarios and make decisions based on the risk-return profile.
An interest rate indicates the opportunity cost of investing funds into one avenue over another, helping investors and businesses assess whether they receive enough return for the risks they take.

Cash Flow

Cash flow is the amount of money generated or expended by a project or business over a specific period.
Analyzing cash flow is vital because it shows how well a company manages its finances. In Haney's case, the pig farm generates a constant annual cash flow of $50,000.
In contrast, switching to residential use would generate $20,000 per year, indicating a shift in cash flow due to operational changes.
By calculating the NPV of these expected cash flows, stakeholders determine the profitability and sustainability of different uses for Haney's property.
Cash flow analysis helps Haney and other economic agents understand the prime factors affecting the value and outcome of their strategic decisions, ensuring that financial resources are effectively allocated.