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

MCB_{0} = 15-q_{0} -5

MCB_{1} = 15-q_{1} -5

[1] Equation to solve dynamically efficient allocation :
MCB_{0} =PV*MCB_{1}

15-q_{0} -5= 15-q_{1} -5 [1/1.07]

[2]

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

15-q_{0} -5= 15-q_{1} -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-q_{0} -5

15- 5.169 -5 = 15.169

*********PLEASE UPVOTE AS SMALL TOKEN OF APPRECIATION********

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