EC238 Lecture Notes - Lecture 18: Dynamic Efficiency, Marginal Cost, Marginal Utility

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28 Oct 2020

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If supply is sufficient to meet demand, then a static efficient solution will provide the optimal allocations over time, regardless of the discount rate. Ie, if the total supply of a depleteable resource were 30 or more, what will the efficient quantities be for each period. As shown by the demand curve, 15 units of resources would be used in period 1 and 5 units in period 2. If supply is not sufficient we must determine the optimal allocation using the dynamic efficiency criterion: maximize the present value of net benefits. The present value for a 2 period model is the sum of the present values in each of the 2 years. The pv in each period is the portion of the area under the demand curve and above the supply curve or the area under the marginal net benefit curve (which is the demand curve minus the marginal cost).

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2. Suppose a demanding schedule is P = 100 - Q and a supply schedule is P = 20 + 2Q. What is the marginal net benefit curve?

MNB = 80 - Q

MNB = 80 - 3Q

MNB = 80 + Q

MNB = 120 - Q

MNB = 120 - 3Q

3. Suppose a demand curve is Q = 100 - P and a supply curve is Q = 0.5P - 25. What is the marginal net benefit curve?

MNB = 75 - 0.5Q

MNB = 125 - 1.5Q

MNB = 125 + 1.5Q

MNB = 50 + 3Q

MNB = 50 - 3Q

5. In a two time-period example, economic efficiency is maximized when ...

The marginal net benefits are maximized in both time periods

The discount rate is set equal to the marginal benefits

The marginal net benefit in the first time period is set equal to the present value of marginal net benefits in the second time period

The marginal net benefits in the first period are set equal to the discount rate in the second time period

The marginal net benefits in the first period are set equal to the user costs in the second time period

6. Assuming economic efficiency is maximized, when will more of a resource tend to be used in the first time period (as compared to future time periods)?

Whenever the discount rate is positive

Whenever the marginal net benefits in the present are positive

Whenever the discount rate is zero

Whenever the user costs are positive in the present

Whenever the marginal net benefits in the future are negative

yellowgnu384

The inverse demand curve for a product using resource X is given by

P = 60 â 0.2Q and the cost of production is constant at

MC = 10

Find the static equilibrium for this product (recall at equilibrium Supply equates Demand and in this case Supply = Marginal Cost) in a single time period (call this t0).

At equilibrium S = D and S = MC = 10

So you should be able to solve these equations simultaneously to find Q

Draw the static equilibrium.

Equilibrium, you will recall, in a static sense is simply where demand equals supply. Now that you know the equilibrium Q you should be able to draw where supply crosses demand (the price should just line up with S and MC because they are flat in this case).

What is the value of consumer surplus from consumption in t0? (recall, this is simply the area under the demand curve and above the price, which now equates Marginal Cost)

This should be a matter of measuring the area of a triangle (i.e. half a square â height* width*0.5).

Imagine that resource X is infinite in supply or perfectly renewable and that the demand and supply curves are unchanged between years.

Consider the following supply and demand equations for a depletable energy resource, with subscripts representing the time period. D0=100-2Q0 S0=50 : D1=100-Q1 S1= 30

A) If the discount rate is 2%, and the total stock of the resource at the beginning of time period 0 (Q-bar) is 90 units, determine the allocation of Q in each period that maximizes the net present value of total benefits (NPVTB) across both periods. This is known as the optimal allocation or dynamically efficient allocation.

B) Calculate the scarcity rent associated with your answer in part a.

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EC238 Lecture Notes - Lecture 18: Dynamic Efficiency, Marginal Cost, Marginal Utility

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