Do not take the work if you cant do it, please. And i dont accept incomplete and BS answers,
Economics 3000H ? 2015/16
Due: April 1, 2016. Please ensure your answers are legible.
1. Consider an exchange economy with two people, A and B, with the following utilty
= 2 2 . Their endowments are as
XA = 8 YA = 8 XB = 12 YB = 4
a. At the endowment point, what are the Marginal Rates of Substitution for A
b. Suppose we establish competitive markets for the demand and supply of
goods X and Y. Using the price of good Y and the numeraire (i.e., set Py =
1), solve for the equilibrium price and allocation.
c. Explain why the competitive allocation is Pareto optimal.
2. Consider a 2?2?2 economy with goods X and Y, factors K and L, and consumers A
and B. The two consumers decide to form a government and finance its activities
through an excise tax on good X. Using the equalities that link competitive outcomes
to Pareto efficient allocations, explain why a tax on only one of the goods will result
in Pareto inefficiency. Does the economy produce too much or too little X?
3. Two types of firms emit gunk, a nasty pollutant. There are five firms of each type.
These firms think of ?gunk emissions? as a productive input much like any other
input. The primary difference is that the price of gunk emissions is currently $0.
Their marginal abatement costs for gunk emissions are
w1 = 120 ? z1 and w2 = 180 ? z2 where wi is the price a type i firm will pay
to emit a unit of gunk and zi is the amount of gunk.
a. Given the current price of gunk emissions, how much does each firm emit
and what are total emissions?
b. Suppose that we want to reduce total emissions to 500 units using a tax of T
per unit of gunk emitted. What value of T will achieve the target level? Are
the 500 units of emissions allocated efficiently among the 10 firms?
c. Suppose instead that each of the 10 firms is given the right to emit 50 units of
gunk and that firms are allowed to buy and sell these rights. What is the
aggregate demand for emissions? What is the aggregate supply of
emissions? Think of each firm as supplying 50 units. What is the competitive
equilibrium price and allocation of gunk emissions? Are the 500 units
allocated efficiently among the 10 firms?
d. Finally, consider a standards approach in which each of the 10 firms is
permitted to emit no more than 50 units of gunk and are not allowed to trade
in permits. Are the 500 units allocated efficiently among the 10 firms?
4. Mosquito control is non-rival and non-excludable. Suppose the economy consists of
two people who are identical and have the following inverse demand for mosquito
P = 50 ? y
where y is the quantity of control. The cost of mosquito control is $20 per unit.
a. What is the socially optimal level of mosquito control?
b. Suppose that the government does not provide mosquito control. How much
mosquito control would individual 1 provide if she believes that individual 2
will not provide any control? How much would she provide if she believes
individual 1 will provide 10? How much if she believes individual 2 will
provide 30 units?
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