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Economics 3000H ? 2015/16

 

Assignment #4

 

Due: April 1, 2016. Please ensure your answers are legible.

 

(10 marks)

 

1. Consider an exchange economy with two people, A and B, with the following utilty

 

1/3

 

functions:

 

=

 


 

= 2 2 . Their endowments are as

 


 

follows:

 

XA = 8 YA = 8 XB = 12 YB = 4

 

a. At the endowment point, what are the Marginal Rates of Substitution for A

 

and B?

 

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.

 

(5 marks)

 

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?

 

(10 marks)

 

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?

 


 

1

 


 

(5 marks)

 

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

 

control:

 

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?

 


 

2

 


 

 


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