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Consider a two period production and investment model. There is an representative consumers only live for...

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Economics

Consider a two period production and investment model. There is an representative consumers only live for 2 period. Utility is given as : U(c) = lnc0 + lnl0 + βlnc1 + βlnl1 where c0, c1 is the consumption, β is time discount factor, l0, l1 is the leisure. The consumer has h units of labor in each period, consumer can work at wage wt . And consumer can save and borrow at r (r is endogenously decided by the market) There is a representative firm only operate for 2 period and owned by consumer. It has production function zF(K, N) = zKαN(1−α) . And it can invest in capital follows Kt+1 = (1 − δ)Kt + It . The cost of investment is 1. The firm has initial capital K0. And firm can save and borrow at r. Let πt be the profit of firm at t (a) (6pt)Write down consumer’s problem (including maximization and constraints)

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