University of California Berkeley Economics and Demand Questions

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I’m working on a economics multi-part question and need an explanation and answer to help me learn.

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Economics 131 Problem Set 4 ? Due November 23rd
– Question 1 (just this page) will be graded on a ?,?+,?? scale; please include the steps and logic you used in your
answer. You can upload your answers to Gradescope until 11:59pm pacific time. Either write directly on this page or
use a blank piece of paper, clearly indicating the part numbers. The questions on the second page are not graded and do
not need to be submitted, but will be important in studying for the final.
1. Consider the following two-period extraction problem (assume a zero discount rate):
Supply (marginal cost of extraction): MC1 = 4 MC2 = 2
Demand (marginal benefit of consumption): MB1 = 10 – Q1 MB2 = 12 – Q2
Total supply of the resource: 10
a) What quantities and prices solve the dynamic efficiency problem, considering both time periods?
b) Suppose government imposes a tax of $8 for each unit of the resource, starting in time period 2.
Solve for the new prices and quantities in each time period.
c) Find the level of the tax such that increases in the tax do not change Q1, but decreases in the tax
do change Q1.
d) How do your answers to parts (a) and (b) change if the resource is not scarce? For example
suppose total supply of the resource is 1000.
2. Scarcity rents:
a) Explain in one or two sentences why the green paradox is unlikely to be a problem if we observe
the current market price of a fossil fuel equals its extraction cost. Why does the key mechanism not
work in this case?
b) Which fossil fuel resources have the highest scarcity rents (making the green paradox most
likely to apply)? Which have the lowest scarcity rents?
3. Consider the following function reflecting the productive capacity of capital. The function takes
three types of capital (natural, human, and reproducible) and combines them to measure overall
productive capacity of the economy in a given year.
Kcapacity = KN + KH + KR
Suppose the earth currently has 100 units of KN, 5 units of KH and 5 units of KR.
a) What is the level of Kcapacity?
b) If we destroy one unit of natural capital in 2021 and increase human capital (through
education) by two units, what will Kcapacity be for 2022? Were we acting sustainably in 2021
according to this model of capital capacity?
c) Explain why economists refer to this as a “weak” model of sustainability. In your explanation,
consider what options humanity has if it destroys all 100 units of the natural capital the earth
started with.
Discussion questions (Keohane and Olmstead):
Chapter 6: 2, 5

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demand curve

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