Question

To anticipate subsequent chapters where more complicated renewable resource models are introduced, consider a slight modification of the twoperiod depletable resource model. Suppose a biological resource is renewable in the sense that any of it left unextracted after Period 1 will grow at rate \(k\) Compared to the case where the total amount of a constant- \(M E C\) resource is fixed, how would the efficient allocation of this resource over the two periods differ? (Hint: It can be shown that \(M N B_{1} / M N B_{2}=(1+k) /(1+r),\) where \(M N B\) stands for marginal net benefit.

Short answer

Answer: The efficient allocation of a renewable biological resource over two periods depends on the relationship between the growth rate of the resource (k) and the interest rate (r). If the growth rate is greater than the interest rate, it is more beneficial to allocate a larger portion of the resource towards Period 1. If the growth rate is smaller than the interest rate, it is more efficient to allocate a larger portion of the resource towards Period 2. In contrast, the efficient allocation of a fixed constant-MEC resource is found by equating the Marginal Net Benefits in both periods.

Step-by-step solution

Define Marginal Net Benefit (MNB) for Renewable Resource

Marginal Net Benefit (MNB) represents the additional benefit derived from using an extra unit of the resource, after taking into account the cost of using it. In the context of a renewable resource, MNB takes into account not only the immediate benefits and costs of using the resource but also the future value of the resource, considering its growth and the interest rate.

Find Relationship between MNB, Growth Rate (k) and Interest Rate (r)

The hint given in the exercise shows that the ratio of MNB in Period 1 to MNB in Period 2 can be written as: \(\frac{MNB_1}{MNB_2} = \frac{1+k}{1+r}\) Here, \(MNB_1\) and \(MNB_2\) are the Marginal Net Benefits in Period 1 and Period 2, respectively, while k is the growth rate of the renewable resource and r is the interest rate.

Compare Efficient Allocation of Renewable and Constant-MEC Resources

For a constant-MEC resource, the total amount of resource available is fixed, and the efficient allocation would be found by equating the MNB in Period 1 and Period 2: \(MNB_1 = MNB_2\) However, for a renewable resource, the allocation is influenced by its growth rate (k) and the interest rate (r), as shown by the ratio: \(\frac{MNB_1}{MNB_2} = \frac{1+k}{1+r}\) If the growth rate (k) is greater than the interest rate (r), the ratio \(\frac{1+k}{1+r}\) will be greater than 1. In this case, it is more beneficial to allocate a larger portion of the resource towards Period 1, since the resource's growth outweighs the interest rate. On the other hand, if the growth rate (k) is less than the interest rate (r), the ratio will be less than 1, which means it is more efficient to allocate a larger portion of the resource towards Period 2, as the interest rate outweighs the resource's growth. In conclusion, the efficient allocation of a renewable resource over two periods differs from that of a constant-MEC resource. It depends on the relationship between the growth rate of the renewable resource (k) and the interest rate (r), with larger allocations in Period 1 if the growth rate is greater than the interest rate and larger allocations in Period 2 if the growth rate is smaller than the interest rate.

Key concepts

Understanding Marginal Net Benefit (MNB)

Marginal Net Benefit (MNB) is a critical concept in renewable resource economics. It defines the incremental benefit gained from the consumption of one more unit of a resource, while factoring in the cost to obtain or use that unit.

When we look at the MNB of a renewable resource, it is essential to consider the future potential of that resource as well. A tree, for example, if left unharvested, will grow and can potentially provide more wood in the future. Therefore, when calculating the MNB, the growth rate of the resource and the interest rate that reflects the opportunity cost of not utilizing the resource now, are crucial elements.

In simple terms, MNB puts a number on the 'worth' of using a resource immediately versus letting it grow or saving it for the future. It's a balance between immediate gratification and long-term benefits, much like choosing between spending money now or investing it for a higher return later.

Resource Growth Rate's Impact on Resource Economics

The resource growth rate, often denoted by the variable 'k', measures how quickly a renewable resource increases in quantity or quality over time.

This rate is significant because it can shift the balance of how resources are allocated over time. Picture a fish population that grows rapidly each year. If we harvest too many fish this year, we might reduce the population. However, if we harvest too few, we miss out on the potential gains from the fish that could have been caught without harming the population's ability to recover.

A higher growth rate suggests that it might be more economically sensible to leave more of the resource unutilized in the short term because the future benefits due to growth outpace the immediate gains from extraction.

The Role of Interest Rate in Resource Allocation

The interest rate, marked as 'r', serves as the benchmark for the cost of current consumption versus future benefits.

Let's translate this into a real-world scenario. If you have a sum of money, the interest rate helps determine whether it's more advantageous to invest it or spend it. Apply the same logic to resources: if the interest rate is high, future benefits need to be significantly larger to warrant delaying resource extraction.

In renewable resource economics, when the resource's growth rate is lower than the interest rate, the incentive increases to use more of the resource sooner rather than later because the opportunity cost of not using the resource (or the money, in our analogy) is higher due to potentially higher returns elsewhere.

Efficient Resource Allocation Across Periods

Efficient resource allocation is about optimizing the timing and amount of resource use to maximize overall benefits across multiple periods.

For a non-renewable resource with a constant supply, we would simply use the resource at a rate that equilibrates MNB across time—ensuring consistent benefit. In the case of a renewable resource, we must also weigh in the growth rate and the interest rate.

If the resource grows at a rate higher than the interest rate, we can infer that there's an incentive to save more of the resource for future use. Contrarily, if the interest rate outdoes the growth rate, we should use more of the resource now, as it's economically preferable. Efficient allocation is all about balancing these variables to ensure that we are getting the maximum possible benefit from our resources over time.