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Econ 6021

Coursework

All answers need a short but complete justification including “workings”.

Questions a)-f) and to some extent g) are variations of familiar themes, h)-j) may be more challenging required only for highest possible marks.

Consider an exchange economy with 2 consumers whose preferences and endowments are represented by:

a) (5%) Is consumer A’s preference strongly monotonic? Is it strictly monotonic?

b) (20%) Suppose, in sub-questions b and c only consumers do not have an endowment, but are given income . What is their demand and respectively ?

c) (5%) Compare (Which is larger?). Discuss your finding.

d) (20%) Now find a Walrasian equilibrium price vector (you can restrict attention to p >> 0).

e) (10%) Find the corresponding equilibrium allocation.

f) (5%) Can you achieve the allocation ((10,10),(90,140)) as Walrasian equilibrium after some transfers?

g) (10%) Suppose from now there is a firm, owned entirely by consumer A, that can produce good 2 from good 1 according to technology . What are the profits of the firm if it produces nothing? At the equilibrium prices you have found in b), if the firm uses just one unit of good 1 as input, what profits does it make? What will be the supply (the profit-maximising output) of the firm for good two at these prices?

h) (5%) Find an equilibrium of this 2 consumer, 1 firm economy. Hint: Make an edu-cated guess using your insights from g) and d) and verify it.

i) (10%) Suppose you are a social planner that contemplates to interfere with this market economy, but you would do so only if this interference has no “losers”. Rela-tive to the equilibrium you found in h), is there an allocation that is feasible (can be achieved with the resources and production possibilities in this economy) and makes both consumers strictly better off?

j) (10%)Suppose now consumer A and B lives in different countries (a and b), the firm is located in country a and the government of country a prohibits all trade between those countries. There are no other resources/consumers/firms in this world. Can consumer A be better off when country a chooses to isolate in this way?