Suppose the MWTP in periods 1 (now) and 2 (one year from now) is given by P = 8-

Question

Suppose the MWTP in periods 1 (now) and 2 (one year from now) is given by P = 8-0.4q. Marginal extraction cost = $3 in period 1 and marginal extraction cost equals $3 in period 2. Let r = 20%. The available supply is 20 units, Determine the allocation of outputs across the two periods that maximize the present value of the net benefits for the use of the resources using the attached engineering graph paper. Show your work on the graph. What is the value of the MUC? Show it on the graph. Intuitively explain what MUC is, using the solution found for this problem

Explanation / Answer

The Marginal willingness-to-pay (MWTP) is the maximum price the individual would be willing to pay for the next unit of the good or service.

Let’s consider that the marginal willingness to pay is given by the constant formula P = 8 – 0.4 q and marginal cost is constant at $3. Now assume following parameters values; a= 8, c = $3, b = 0.4, Q = 20 and r = 0.20

Using these we obtain: 8 – 0.4 q1 –3 – = 0 (1)

(8- 0.4q1 –3 – )/1.20 = 0 (2)

q1 + q2 = 20

The solution of the equations give the results: q1 = 10.238, q2= 9.762, = $0.905.

The present value of marginal user cost is represented by .

The equatioThe equation (1) states that price in the first period (8 – 0.4 q 1 ) should be equal to the sum of marginal extraction cost ($3) and marginal user cost ($0.905).

Multiplying (2) by (1+r), it becomes clear that price in the second period (8 - 0.4q 2) is equal to the marginal extraction cost ($3) plus the higher marginal user cost (1+r) = (0.905) (1.20) = $1.086.

The total marginal cost of the first resource would rise until it equaled that of the second resource at the time of transition. In the period of time prior to transition (T*) only the cheapest resource would be consumed.

Two salient observations: (1) The transition is smooth; total marginal cost never jumps to a higher level.

(2) The rate of increase in total marginal cost slows down after the time of transition.

(1) The total marginal cost of the two resources have to be equal at the time of transition, otherwise net benefits could be increased by switching over to lower-cost resource. In period before transition, the first resource is cheaper. After transition it is exhausted.

(2 )The components of the TMC that is growing (the marginal user cost) represents a smaller portion of the TMC of the second resource than of the first resource. in both cases the marginal user cost is increasing at rate r, and the marginal cost of extraction is constant. Economics of Natural Resource

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