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Assume that an economy has two firms that use a production function that satisfies the properties of "our" production model. (1) Assume that the level of TFP is exogenous, and that each firm is stuck with a given level of capital(K). Finally assume that labor can be re-allocated at any time. Explain why equalizing the marginal products of labor is consistent with an efficient allocation. (2) Assume two firms with an identical Cobb-Douglas production function and the same level of TFP. Show that the efficient allocation is achieved when both firms have the same capital-labor retie? Does this imply that both firm employ the same quantities of K,N? (3) Imagine an economy where a state-owned enterprise (SOE) exists alongside a private firm that products the same good. The private firm has a TFP level that is three times as high as the SOE: Ap=3*As. The production function are Yp=Ap*Np and Ys=As*Ns, where Np+Ns=1. The SOE employs three quarters of the work force (Ns=3/4) (i) What is the efficient allocation of labor in this economy? (ii) What is the TFP level for the economy relative to the level associated with the efficient allocation?
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