Suppose a fossil fuel has stable demand and a constant marginal cost. There are only two periods. MB = 8 – 0.4q; and MC = 2. Suppose there are only 20 units of the resource and the discount rate is r = 0.10. Solve for the dynamic optimum across periods. Show your mathematical solution, but also depict it graphically (ACCURACY COUNTS) using the double-vertical axes model from class.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter5: Business And Economic Forecasting
Section: Chapter Questions
Problem 1.1CE
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#2. You have two periods. I've given you an externality with MEC=0.05q1. So, 

MB1=8-0.4q1

MB2=8-0.4q2.

So, the externality is a cost realized in period 2 but caused by period 1's production choice. Q1 belongs to the first period, and Q2 is the second. 

Suppose a fossil fuel has stable demand and a constant marginal cost. There
are only two periods. MB = 8 – 0.4q, and MC :
the resource and the discount rate is r = 0.10. Solve for the dynamic optimum across
periods. Show your mathematical solution, but also depict it graphically (ACCURACY
COUNTS) using the double-vertical axes model from class.
a. For help, you can view the solutions for CH5 Self Test 1 and 2 which solve two-
2. Suppose there are only 20 units of
period models with different setups.
Draw again (ACCURATELY) the double-vertical axes model using the curves
and constraints from #1. Suppose we are modeling fossil fuel use and the use of the
resource causes a negative externality. For example, the amount we burn in period 1
contributes to the negative effects of global warming in period 2. So, let MEC = 0.05q1.
Solve for the new dynamic optimum in the presence of the externality.
Transcribed Image Text:Suppose a fossil fuel has stable demand and a constant marginal cost. There are only two periods. MB = 8 – 0.4q, and MC : the resource and the discount rate is r = 0.10. Solve for the dynamic optimum across periods. Show your mathematical solution, but also depict it graphically (ACCURACY COUNTS) using the double-vertical axes model from class. a. For help, you can view the solutions for CH5 Self Test 1 and 2 which solve two- 2. Suppose there are only 20 units of period models with different setups. Draw again (ACCURATELY) the double-vertical axes model using the curves and constraints from #1. Suppose we are modeling fossil fuel use and the use of the resource causes a negative externality. For example, the amount we burn in period 1 contributes to the negative effects of global warming in period 2. So, let MEC = 0.05q1. Solve for the new dynamic optimum in the presence of the externality.
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