Question

In this problem you will compute the dynamically efficient allocation of a depletable, non-recyclable resource. To answer the questions below, assume the following:

• Allocate resource between two time periods t=1,2
• The fixed supply of the resource is 10 barrels
• Demand is same in both periods and given by P_t = 15 – q_t
• Marginal cost of extracting the resource is the same in both periods and is given by MC_t=$5
• The discount rate is 7%

1. What is the equation that must be satisfied to solve for the dynamically efficient allocation of this depletable resource between periods 1 and 2? Please enter this equation in the 1st box below.

2. What is the dynamically efficient allocation of this resource in period 1? Please enter this number rounded to the hundredths place in the 2nd box below.

3. What is the dynamically efficient allocation of this resource in period 2? Please enter this number rounded to the hundredths place in the 3rd box below.

4. Compute the marginal user cost in period 1 and enter it in the 4th box below. Please round this number to the hundredths place.

5. In 1-2 sentences, explain in your own words what the marginal user cost represents. Write your answer in Word or Google Docs then copy and paste it into the 5th and last box below.

Answer 1

Given, Demand ,  P_t = 15 – q_t

Marginal cost of extraction , MC_t=$5

The discount rate is 7%

Total supply = 10 barrels

MCB₀ = 15-q₀ -5

MCB₁ = 15-q₁ -5

[1] Equation to solve dynamically efficient allocation : MCB₀ =PV*MCB₁

15-q₀ -5= 15-q₁ -5 [1/1.07]

[2]

&[3]  the dynamically efficient allocation of this resource in period 1:

15-q₀ -5= 15-q₁ -5 [1/1.07]
_{substituting q1 +q0 = 10, or q1 = 10- q0}
q0 = 1070/207 = 5.169

q1= 1000/207 = 4.831

[4] Marginal cost of user = price - MC

for period 1 : 15-q₀ -5

15- 5.169 -5 = 15.169

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