2. General Equilibrium. Consider a representative consumer that lives two periods with utility fu…

2. General Equilibrium. Consider a representative consumer that lives two periods with utility function U(Cl)-(log(q) + ?,) + ?(log(q) + ? ), where 0 < ? < 1 is a discount factor, ? > 0 and ? > 0 are param- eters (constants). c is consumption and 1 is leisure (the numbers denote the period). The consumer chooses consumption, how much to save for period 2, i.e. b2, working hours N in each period, receives a wage w and dividends ?, the tine constraint is 24-1 + N. Additionally, the con- sumer pays a labor income tax t in periods 1 and 2. Finally, Government expenses are G The representative firm has technology zF(K,N)KN Produces for two periods, chooses labor and investment subject to K2(1-5) Ki+ I2. Suppose that the representative firm is endowed with K1, that is, in period 1 the firm has Ki (notice that the firm only chooses capital for period 2) Write the intertemporal budget constraint ·Write the consumers problem. . Find the first order conditions for the consumer (dont forget the budget constraint) Hint: derive the following conditions: . Explain the economic meaning of the conditions above. . For which values of ? and ? is the marginal utility of leisure decreas- ing? What happens with the solution of the problem if the marginal utility of leisure is decreasing? Write the firms problem . Find the first order conditions for the firm (MP1, MPN2- w2 and MC(2) MB(I. Remember that the firm maximizes the present value of profits: subject to K2 (1- 5)Ki I2 You can solve for 12 and use it in V to solve the optimization problem without constraints. . Explain the economic meaning of the conditions above.” src=”https://files.transtutors.com/questions/transtutors004/images/transtutors004_b94521da-3986-402c-9f68-c3e951004fb7.png”></p>
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<p> 2. General Equilibrium. Consider a representative consumer that lives two periods with utility function U(Cl)-(log(q) + ?,) + ?(log(q) + ? ), where 0 0 are param- eters (constants). c is consumption and 1 is leisure (the numbers denote the period). The consumer chooses consumption, how much to save for period 2, i.e. b2, working hours N’ in each period, receives a wage w and dividends ?, the tine constraint is 24-1 + N”. Additionally, the con- sumer pays a labor income tax t in periods 1 and 2. Finally, Government expenses are G The representative firm has technology zF(K,N)KN Produces for two periods, chooses labor and investment subject to K2(1-5) Ki+ I2. Suppose that the representative firm is endowed with K1, that is, in period 1 the firm has Ki (notice that the firm only chooses capital for period 2) Write the intertemporal budget constraint ·Write the consumers problem. . Find the first order conditions for the consumer (don’t forget the budget constraint) Hint: derive the following conditions: . Explain the economic meaning of the conditions above. . For which values of ? and ? is the marginal utility of leisure decreas- ing? What happens with the solution of the problem if the marginal utility of leisure is decreasing? Write the firm’s problem . Find the first order conditions for the firm (MP1, MPN2- w2 and MC(2) MB(I. Remember that the firm maximizes the present value of profits: subject to K2 (1- 5)Ki I2 You can solve for 12 and use it in V to solve the optimization problem without constraints. . Explain the economic meaning of the conditions above. </p>
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