Microeconomic advanced walrasian equilibrium

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NonCanada is a country unsure about its immigration policy. It is inhabited by a lone capitalist endowed with K units of generic capital, which he can transform one-to-one into a consumption good. NonCanada has no labour to begin with. If the government adopts policy s, then the country admits up to measure Ws of willing skill-s immigrants (and only these immigrants), where s\varepsilon S\equiv (1,2) indexes the skill level: low (s = 1) or high (s = 2). The government announces that policy s will be adopted with probability p_{s}\epsilon (0,1)where p1 +p2=1. Denote p\equiv (p_{1,},p_{2}) . Each skill-s immigrant can either work for the capitalist in NonCanada at the going wage ws or remain in his home country and earn \gamma _{s} there. Each type of labor requires skill-specific capital, which the capitalist can produce one-to-one from his endowment of the generic capital. For any s\varepsilon S, for some coefficients a_{s}\varepsilon (0,1) and b_{s}>0 units of skill-s specific capital and hs units of skill-s labor can be transformed into min(\frac{k_{s}}{a_{s}}, \frac{h_{s}}{b_{s}})

units of the consumption good.

Assume that Ws>(bs*Ks)/as and\gamma _{s}<(1-a_{s})/b_{s} for all s\varepsilon S Before—and only before—the uncertainty about the immigration policy is resolved, the capitalist, an expected-profit maximizer, transforms some of his genericcapital into skill-specific capital. Then the policy uncertainty is realized, the immigrant labor arrives, and the capitalist chooses how much labor to hire, at the prevailing Walrasian equilibrium ws. As a result, the capitalist’s expected profit is:

1. Explain the terms in the expression for the capitalist’s profit in the display above.

2. Solve for the capitalist’s optimal investment in capital as a function of p and the anticipated Walrasian-equilibrium wages (w1,w2).

3. Compute the anticipated Walrasian-equilibrium wages (w1,w2). What is the capitalist’s profit when no uncertainty about the immigration policy exists, that is, when ps = 1 for some s\varepsilon S

4. Show that there exists an uncertain immigration policy that is worse for the capitalist than any certain policy. That is, show that one can find a p such that \prod (p)<min\prod (0,1), \prod (0,1)

5. When \prod (p)<min\prod (0,1), \prod (0,1) can one conclude that eliminating uncertainty about the immigration policy constitutes a Pareto improvement in NonCanada?

    • 7 years ago
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