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EconS 301, Microeconomics with Calculus
Spring 2015, Homework 11
1. Explain why universal percentage taxes do not make an economy Pareto inefficient, but universal per unit taxes do.
(Hint: Start with the Pareto efficient conditions that MRS=MRT=price ratio between good. Think about how
percentage taxes and per unit taxes impact the price ratio.) (3 points)
2. Currently about 16-17% of GDP in the US is spent on health care. Many economists argue that health insurance and
subsidized health care artificially increase the demand for health care by lowering the effective price consumers must
pay, leaving the allocation of resources between health care and other goods Pareto inefficient. Using an Edgeworth
box diagram that includes the PPF, analyze this problem from the perspective of general equilibrium and welfare
economics. Specifically discuss:
a. How health insurance causes too much of our economy to be devoted to health care; (2 points)
b. Health insurance and subsidized health care means that there is an equivalent to an income transfer from
health people to sicker people. Assume in your (two-person Edgeworth box economy) the initial endowment
is equal, so both start in the middle of the Edgeworth box. Suppose one person is sickly and the other healthy,
but both must by health insurance. If the two goods in your economy are “healthcare” and “other goods”
explain what how an insurance requirement will redistribute income and leave the economy Pareto
inefficient. (3 points)
3. Analyze this question from the perspective of Pareto efficiency: Simpson has found $2000 and decides to divide it
between his two children, Sara and Bill. Consider what is necessary (in terms of their marginal utility of wealth) for
each of the following distributions to be Pareto efficient.
a. Giving each $1000. (1 point)
b. Allocating it so each child’s share is inversely proportionate to his or her wealth. (2 points)
4. Consider a pure endowment economy (no production) with two goods, A and B, and two people, Sue and Bill. There
are a total of 4 units of good A and 8 units of good B.
a. Draw the Edgeworth Box for this economy. (1 point)
b. Suppose Bill has 5 units of B and 1 unit of A. Show this allocation on your graph? (1 point)
c. Both Bill and Sue have fixed proportion utility functions, so U=min(2A,B). What is the ratio of A and B they
each want to consume? (1 point)
d. Find the contract curve for this economy, and mark it on your graph? (2 points)
e. Show the part of the contract curve that would improve both Bill’s and Sue’s utility. Explain why this is the
relevant portion. (2 points)
f. Suppose Bill still has the fixed proportion utility function, but Sue has a simple Cobb-Douglas production utility
function of the form U=A*B. Now find the contract curve. Why is it unchanged? What will be Sue’s MRS? (3
points)
5. Consider a two-person economy (Al and Sue) with two goods (A and B) where both individuals have a utility function
U=A*B. The PPF for A and B is a straight line with a constant MRT. With the resources in the economy, at most 20
units of B can be produced, and at most 10 units of A.
a. What is the MRT in this economy? (1 point)
b. Find the formula for the MRS for each person. (1 point)
c. How much A and how much B will be produced if the economy is Pareto efficient? Explain. (Hint, remember
we need the MRS=MRT.) (2 points)
XC1. Add production in question 4. If the economy is Pareto efficient, what will be MRT. Explain. (3 points)
XC2: In question 5, suppose Al can produce only A and Sue can produce only B.
a. Draw the Edgeworth box of question 5 that illustrates efficient production and the initial allocation. (2 points)
b. Show the exact point at which they will end up. Explain why they end up there. (3 points)