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i. To allocate 40 units between two periods in a dynamic efficient allocation, we need to find the optimal quantities that equate the present value of marginal net benefits (MNB) in each period. Given the inverse demand function P = 25-0.4q and the marginal supply cost of £5, the marginal net benefit in period t is MNBT (25-0.4qt-5)(1 + r)t-1. The dynamic efficient allocation must satisfy the necessary condition PV(MNB1) = PV(MNB2)=λ, where A is the present value of marginal user cost. Let q1 and q2 be the quantities allocated to periods 1 and 2, respectively. Then, the present value of marginal net benefits in each period is: = PV(MNB1) (25-0.4q1-5) (1+r) PV(MNB2) (25-0.4q2 -5) Since PV(MNB1) = PV(MNB2) = λ, we have: (25-0.4q1-5)(1+r) = 25-0.4q2 - 5 =λ Solving this system of equations, we get: q1= 14.44 (rounded to two decimal places) q2=25.56 (rounded to two decimal places) Transcribed Image Text: Suppose the inverse demand function for a depletable resource is linear, P = 25 - 0.4q, and the marginal supply cost is constant at £5. i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working

i. To allocate 40 units between two periods in a dynamic efficient allocation, we need to find the optimal quantities that equate the present value of marginal net benefits (MNB) in each period. Given the inverse demand function P = 25-0.4q and the marginal supply cost of £5, the marginal net benefit in period t is MNBT (25-0.4qt-5)(1 + r)t-1. The dynamic efficient allocation must satisfy the necessary condition PV(MNB1) = PV(MNB2)=λ, where A is the present value of marginal user cost. Let q1 and q2 be the quantities allocated to periods 1 and 2, respectively. Then, the present value of marginal net benefits in each period is: = PV(MNB1) (25-0.4q1-5) (1+r) PV(MNB2) (25-0.4q2 -5) Since PV(MNB1) = PV(MNB2) = λ, we have: (25-0.4q1-5)(1+r) = 25-0.4q2 - 5 =λ Solving this system of equations, we get: q1= 14.44 (rounded to two decimal places) q2=25.56 (rounded to two decimal places) Transcribed Image Text: Suppose the inverse demand function for a depletable resource is linear, P = 25 - 0.4q, and the marginal supply cost is constant at £5. i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working

Microeconomics: Principles & Policy
Microeconomics: Principles & Policy
14th Edition
ISBN:9781337794992
Author:William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:William J. Baumol, Alan S. Blinder, John L. Solow
Chapter18: Pricing The Factors Of Production
Section: Chapter Questions
Problem 2TY
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In the answer below to my question which is also attached, how is the equation solved? r is given but i don't see how you can solve for q1 and q2 with the equation (25-0.4q1-5)(1+r) = 25-0.4q2 -5 = λ

i. To allocate 40 units between two periods in a dynamic efficient allocation, we need to find the optimal quantities that equate the present value of marginal net benefits (MNB) in each period. Given the inverse demand function P = 25-0.4q and the marginal supply cost of £5, the marginal net benefit in period t is MNBT (25-0.4qt-5)(1 + r)t-1. The dynamic efficient allocation must satisfy the necessary condition PV(MNB1) = PV(MNB2)=λ, where A is the present value of marginal user cost. Let q1 and q2 be the quantities allocated to periods 1 and 2, respectively. Then, the present value of marginal net benefits in each period is: = PV(MNB1) (25-0.4q1-5) (1+r) PV(MNB2) (25-0.4q2 -5) Since PV(MNB1) = PV(MNB2) = λ, we have: (25-0.4q1-5)(1+r) = 25-0.4q2 - 5 =λ Solving this system of equations, we get: q1= 14.44 (rounded to two decimal places) q2=25.56 (rounded to two decimal places)
Transcribed Image Text:i. To allocate 40 units between two periods in a dynamic efficient allocation, we need to find the optimal quantities that equate the present value of marginal net benefits (MNB) in each period. Given the inverse demand function P = 25-0.4q and the marginal supply cost of £5, the marginal net benefit in period t is MNBT (25-0.4qt-5)(1 + r)t-1. The dynamic efficient allocation must satisfy the necessary condition PV(MNB1) = PV(MNB2)=λ, where A is the present value of marginal user cost. Let q1 and q2 be the quantities allocated to periods 1 and 2, respectively. Then, the present value of marginal net benefits in each period is: = PV(MNB1) (25-0.4q1-5) (1+r) PV(MNB2) (25-0.4q2 -5) Since PV(MNB1) = PV(MNB2) = λ, we have: (25-0.4q1-5)(1+r) = 25-0.4q2 - 5 =λ Solving this system of equations, we get: q1= 14.44 (rounded to two decimal places) q2=25.56 (rounded to two decimal places)
Transcribed Image Text: Suppose the inverse demand function for a depletable resource is linear, P = 25 - 0.4q, and the marginal supply cost is constant at £5. i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working
Transcribed Image Text:Transcribed Image Text: Suppose the inverse demand function for a depletable resource is linear, P = 25 - 0.4q, and the marginal supply cost is constant at £5. i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working
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