Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Economics 201 Microeconomics

Tutorial 11

Question 1:

(a) Is it possible to have a Pareto efficient allocation where someone is worse off than (s)he is at an

allocation that is not Pareto efficient? Explain your reasoning.

(b) Is it possible to have a Pareto efficient allocation where everyone is worse off than they would be at another Pareto efficient allocation? Explain your reasoning.

Question 2:

Joe and Ted each consume two goods, X and Y. Joe’s MRS between the two goods is given by (10y)/(x) while Ted’s MRS is given by (10x)/(y) where x and y denote the amounts of Good X and Good Y consumed respectively. Together they have 10 peaches and 10 plums. Verify whether each of the following allocations lies on the contract curve.

Joe: 8 units of x and 9 units of y; Ted: 2 units of X and 1 unit of y.

Joe: 1 unit of x and 1 unit of y; Ted: 9 units of X and 9 units of y.

Joe: 4 units of x and 3 units of y; Ted: 6 units of X and 7 units of y.

Joe: 8 units of x and 2 units of y; Ted: 2 units of X and 8 units of y.

Question 3:

Consider a pure exchange economy with two consumers, A and B, and two goods, x and y. Consumer A has endowment (3, 1). Consumer B’s endowment is (0, 2). Both agents regard goods x and y as perfect (one-for-one) complements.

(a) Depict this situation in an Edgeworth Box.

(b) What is the contract curve for this economy?

(c) What prices are consistent with general equilibrium in this economy? Can you determine the final allocation of goods that will result from market exchange at equilibrium prices?

(d) How would your answers to (a) – (c) change if B regarded x and y as perfect (one-for-one) substitutes?

Question 4:

The market for widgets is characterized by the following demand and supply curves. Demand: P = 120 – 2Q and supply: P = Q. But the production of widgets generates an externality of $6 per unit.

(a) What is the equilibrium price and quantity if producers do not take the externality into account?

(b) How can the producers be made to internalize the externality?

(c) What is the socially optimal price and quantity of widgets?

(d) How much tax revenue does the government raise?

(e) How much of the tax is borne by the buyers and how much by the sellers? Draw a diagram to illustrate your answer and highlight the distinction between the private optimum and the social optimum.

Question 5:

Robinson and Friday are the only two people on an island.  They each survive only on apples and oranges. Robinson has 6 apples and 4 oranges, while Friday has 4 apples and 6 oranges.  Both Robinson’s and Friday’s utility function is U (a, o) = a*o, where “a” denotes the quantity of apples and “o” denotes the quantity of oranges. (i) Suppose Robinson and Friday both consume their initial endowments. Explain why this is not Pareto efficient. (ii) Suggest one re-allocation of apples and oranges that would make both Robinson and Friday better off. This implies that this potential re-allocation must lead to higher utility than if both consume their original endowments. (iii) What does this reallocation imply for the relative price of apples and oranges?