Part 1-

Allow the agent to have an endowment of good 1 equal 2, and an endowment of good 2 equal to the 6.

Derive expressions for the ordinary demands for both goods and calculate the

gross and net demands for each good.

b) An agent has a utility function over wealth given by where c is 8. Their wealth if not robbed is equal to your 26,000.

Should they be robbed, their wealth will be 9000.

They assess the probability of being robbed as 1/30. How much would this agent be prepared to pay for full insurance? How much would they have to pay for full (actuarially) fair insurance?

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Part 2-

Consider the two agents, A and B.

Agent A has the utility function where c is 1and d is 3. Agent A's endowment of good 1 is 2,

and Agent A's endowment of good 2 is 6.

Agent B has the utility function where 'e' is 9 and f is 8. Agent B's endowment of good 1 is 6,

and Agent B's endowment of good 2 is 2.

The price of good 2 is your 8.

a) Find the equilibrium price for good 1 and the gross and net demands of both agents for

goods 1 and 2.

b) Repeat the analysis for the cases where

i. the values of c and d are swapped for A, and e and f are swapped for B.

ii. the endowments of goods 1 and 2 are swapped for A, and the endowments of

goods 1 and 2 are swapped for B [with c, d, e, f at their original - i.e part a)

values].

TIP:

PART 1-

Income is now determined by the value of the endowment. Once that substitution has been made getting the answer is straightforward and this is a straight insurance question

PART 2-

The key here is to remember that part of the solution is a price ratio (p1/p2) but you can't determine both prices individually so proceed on the basis that p2 is fixed at it's given value and try to find p1 as a function of p2.

The gross demand functions for each good are found as in Part 1 using the endowment values (in which p1 will remain a variable). The gross demands for a good from both agents have to add up to the supply which is the amount of the good in the two endowments. This will give you demand curves and a 'supply' condition, both of which have p1 as a variable. Solving for p1 will give you the information you need to solve for all the quantities.