Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present?
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92.86 |
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100 |
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107.14 |
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115.12 |
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none of the above |
We have the following information
Q = 150 – P + 2Y; where Y = 50 for both the periods
So, Q = 150 – P + 100
Q = 250 – P
P = 250 – Q Where P is price and Q is the quantity
Marginal cost (MC) = 0
Total reserves = 200
Discount rate (r) = 10% or 0.1
In the case of indefinite stock, the amount of the resources consumed is determined by the profit maximizing condition of Price = MC. However, in the present case the stock is limited to 200. In a two-period model for an efficient allocation we need to equalize the marginal rent of period one and period two.
P – MC(Q1) = P – MC(Q2)
Now, the marginal profit of a given period has to be equal to the discounted marginal profit of the following period. This is called the “r-percent” rule or Hotelling’s rule and it is given by the following equation
P – MC(Q1) = [P – MC(Q2)]/(1 + r)
What the above equation says is that the marginal profit of a given period has to be r% higher than the marginal profit of the previous period. Solving the above
250 – Q1 – 0 = [250 – Q2 – 0]/(1 + 0.1)
250 – Q1 = (250 – Q2)/(1.1)
(250 – Q1) = 250/1.1 – Q2/1.1
Now the reserve constraint is
Q1 + Q2 = 200
We will replace Q2 = 200 – Q1
(250 – Q1) = 250/1.1 – (200 – Q1)/1.1
(250 – Q1) = 227.27 – 200/1.1 + Q1/1.1
(250 – Q1) = 227.27 – 181.81 + Q1/1.1
275 – 1.1Q1 = 50 + Q1
2.1Q1 = 225
Consumption of the Resources in the present: Q1 = 107.14
Q2 = 200 – Q1
Consumption of the Resources in the next period: Q2 = 92.86
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 in the present but Y = 100 in the future. Let MC = 0. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present? 48.32 55.23 62.44 70.12 none of the above Let demand be given by Q = 150 - P...
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present? 92.86 100 107.14 115.12 none of the above
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present? 92.86 100 107.14 115.12 none of the above
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 400. Consider the basic two-period model. What is consumption of the resource in the future? 92.86 107.14 154.76 200 none of the above
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 400. Consider the basic two-period model. What is consumption of the resource in the future? 92.86 107.14 154.76 200 none of the above
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Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 200. Let there be a backstop technology available at a constant price of $40. Consider the basic two-period model. What is consumption of the resource in the present? 92.86 105.71 107.14 200.00 213.64
Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 30. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present? 94.29 105.71 107.14 111.11 none of the above
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Let demand be given by Q = 150 - P + 2Y. This is the same for all problems of this type. Let r = 10%. Let Y = 50 across both periods. Let MC = 0. Let reserves = 200. Consider the basic two-period model. What is consumption of the resource in the present IF THE OWNER OF THE RESOURCE IS A MONOPOLIST? 94.29 98.81 101.19 105.71 none of the above