Download SPRING 2003 - AED 503 ASSIGNMENT 2

FALL 2014 - AED 4003 ASSIGNMENT 2 – ANSWER GUIDE
Answer all of the questions below. Your answers should be as complete as possible,
using diagrams and written explanations where appropriate. In order to get partial
credit, provide more than a one-or-two sentence answer. Each complete question is
worth 25 points.
(Q1) Suppose in a simple two good/two consumer economy that a policymaker decides
that it would prefer a Pareto efficient market outcome to favor consumer John much
more than it favors consumer Paul, relative to the Pareto efficient market outcome that
would occur given the initial endowments of the two goods. Using an Edgeworth Box
diagram, show how the policymaker could achieve this objective by redistributing the
initial endowment through lump-sum taxes and transfers. State the relevant welfare
theorem that underlies this result. What would happen if the policymaker instead
attempts to achieve their objective by distorting the prices of the two goods at the initial
endowment?
(A1) The best way to answer this question is first to state the Second Welfare Theorem,
i.e., with convex preferences there is always a set of prices that will ensure each Pareto
efficient outcome is a competitive equilibrium. In an Edgeworth Box, you can then
illustrate that this implies the most appropriate way of achieving a Pareto efficient
outcome that favors consumer John compared to consumer Paul is to impose a lumpsum tax on consumer Paul’s initial endowment, and transfer by lump sum to consumer
John’s endowment. Given the new endowment, the market can then be allowed to work
towards achieving the desired Pareto efficient outcome. In other words, once the
relevant endowment has been reached by lump-sum transfers, let the market work
towards the favored Pareto efficient outcome. You should then show that distorting
prices is not the appropriate way of doing this as it will not generate a Pareto-efficient
outcome, i.e., it will result in each consumer being off the contract curve, and there is
excess demand for one good and excess supply for the other.
(Q2) Suppose that production in a two good economy can be described by a concave
production possibility frontier. Describe in your own words what the production
possibility frontier represents. What assumptions would have to be made about
production technology in order for the production possibility frontier to be concave?
How does society choose a particular point on this frontier? Explain how this then
determines the dimensions of an Edgeworth Box of exchange. What conditions have to
be met for there to be simultaneous efficiency in production and exchange?
(A2) The production possibility curve describes the different combinations of output of
the two goods that can be achieved in an economy, given production technology and
fixed supplies of factors of production. Drawing a properly labeled diagram would help
your answer here.
For the production frontier to be concave, it would be necessary to assume that each
good is produced under constant returns to scale with two factors of production, say
labor and capital. Importantly, one good is assumed to be labor intensive in production,
while the other is capital intensive in production. This last assumption, in combination
with the assumption of fixed supplies of the factors of production, and constant returns
to scale, is enough to cause concavity of the production possibility frontier, i.e., as
production of the labor intensive good is reduced, more labor than capital is released for
use in the good that is capital intensive, which given the fixed supply of capital,
constrains production of the capital intensive good.
Society chooses a point on the production frontier through the tangency of a community
indifference curve with the frontier, i.e., where society’s demand for the two goods,
expressed through community indifference curves, is just equal to supply of the two
goods. Remember to explain that the community indifference curves represent the
aggregate preferences of all consumers. Again drawing a properly labeled diagram
would help your answer here.
Once you have found a tangency between a community indifference curve and the
production possibility frontier, this determines how much of each good is to be
produced, which in turn determines the dimensions of an Edgeworth Box of exchange
inside the production possibility frontier. This is best shown in a labeled diagram.
The conditions for simultaneous efficiency in production and exchange are that the set
of relative prices tangent to the production frontier and the community indifference curve
are the same, and hence have the same slope, as the set of prices that are tangent to
the slopes of the two consumers’ indifference curves. Specifically, the slope of the price
line should be equal to the marginal rate of transformation between the two goods,
which in turn should just be equal to the equalized marginal rates of substitution
between the two goods for the two consumers. Again, a diagram will help your answer.
(Q3) Explain carefully why a chemical plant polluting the atmosphere might generate a
negative production externality. Suppose the chemical firm’s cost function C is defined
as Cc(c,x), where c are chemicals produced and x is air pollution from chemical
production. Define what is meant by the marginal costs of producing chemicals and the
marginal costs of abating air pollution. Assume the marginal costs of chemical
production increase with chemical output, and marginal abatement costs decline with air
pollution, and the chemical firm sells in a competitive market. Use the appropriate
diagram to show where the chemical firm will maximize its profits. Explain why if the
firm cuts back its output, its profits decline and its abatement costs increase.
(A3) First, you need to explain that in producing chemicals, the chemical plant causes
air pollution, which in turn causes the marginal costs of other local producers to
increase. This increase in marginal costs, for other local producers, causes them to cut
back output and hence lose profits. The point you need to emphasize is that the
externality comes about because the chemical plant has not been faced with the
economic decision of how much it is willing to pay for the right to pollute the air, i.e., it
fails to account for the true marginal costs of its production activity.
The marginal costs of producing chemicals are the addition to the plant’s costs of
producing one more unit of chemicals - mathematically, this would be ΔCc(c,x)/ Δc. The
marginal costs of abating pollution are the foregone profits to the chemical plant of
reducing its output, and hence pollution, by one unit - mathematically, this would be
ΔCc(c,x)/Δx. The key here is to make sure you get at the idea that the opportunity cost
at the margin of cutting back pollution is measured in terms of lost profits.
The appropriate diagram is one where you draw an upward-sloping marginal production
cost curve, and a downward-sloping marginal abatement cost curve. In addition, as the
plant is operating in a competitive market, it is a price taker, hence it faces a perfectly
elastic demand curve, and its marginal revenue is therefore a flat function given by the
chemical price. Using this diagram, you need to show that profit maximization occurs at
the level of chemical output where marginal production cost is equal to marginal
revenue. This is also equivalent to where its marginal abatement costs are zero, i.e.,
where it does not forgo any profits from its choice of output, and hence pollution. From
this you can show that if it cuts back output, marginal costs fall below marginal revenue,
the plant then loses profits, and hence its marginal abatement costs increase. It will be
helpful here to show the lost profits in the diagram are equivalent to the increased
abatement costs.
(Q4) Suppose there is a hog producer that generates water pollution. MAC are the
firms’ marginal abatement costs, while MPC represent the marginal water pollution
costs to the local population. Using the appropriate diagram, explain how a Pareto
efficient level of water pollution would be achieved if the local population has welldefined property rights over clean water. Would the same Pareto-efficient levels of
water pollution be achieved if the hog producer had the property rights to the clean
water?
(A4) The key to a good answer is to first draw and label the diagram, with upward
sloping marginal pollution costs, and downward sloping marginal abatement costs.
Then you need to lay out how the local population and the hog producer would bargain
to the Pareto efficient level of pollution. Given it is the local population that has the
property rights to clean water, they will be willing to trade those rights up to the point
where their marginal pollution costs are just equal to the marginal abatement costs of
the hog producer. A good answer will point out how pollution costs and abatement
costs are measured by areas underneath the relevant marginal curves, and will get at
the idea of how the hog producer has to compensate the local population for incurring
the costs of pollution, but only up to the Pareto efficient point, after which, the price the
hog producer is willing to pay for the right to pollute is less than what the local
population requires in compensation.
If the property rights are instead owned by the hog producer, then according to the
Coase theorem, the same Pareto efficient level of pollution will be achieved. A good
answer here will get at the idea of how the hog producer has to now be compensated
for incurring the costs of reducing pollution, but only up to the Pareto efficient point, after
which, the price the local population is willing to pay for the clean water is less than
what the hog producer requires in compensation.