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1) Consider a consumer in a two period economy. Denote consumption goods as c1 and c2.

Suppose that this consumer has an endowment of (6,0). Suppose that this consumer has access to markets (where goods 1 and 2 are traded for one another) and that the price ratio is 1 + r.

(a) Assume that this consumer also has access to a technology which allows her to transform x1 units of the period 1 good into x2 = √x1 units of period 2 good. State the consumer's budget set/budget line.

(b) Now assume that a profit maximizing firm operates this technology and that the consumer owns the firm. State the consumer's budget set/budget line in this case.

2) Consider a a two state model. Suppose that there are two consumers, A and B, with

endowments of ωA = (6, 4) and ωB = (8, 6).

Let the objective probability of state 1 occurring be π. Suppose that both consumers are

expected utility maximizers and strictly risk averse and that they have identical preferences πu(c1) + (1 − π)u(c2) with u′(·) > 0, and u′′(·) < 0.

Is there idiosyncratic risk? Is there aggregate risk? Demonstrate/explain.
I claim that neither consumer will be fully insured in the Walrasian equilibrium of this economy. Prove this claim.
What (if anything) can we say about the Walrasian Equilibrium price ratio in this economy?

3) Determine if the area variation measure AV will over- or under-estimate the equivalent

variation EV (focus on the absolute values) for the price decrease of a normal good. Be explicit.