Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total
solve a,b,c
– Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total factor productivity, N D is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0 < t < 1). There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U(c, l) = ln c + ln l (1)
(a) Write down the definition of a competitive equilibrium for the above economy. (
b) Show that the Walras’ law holds for this economy.
(c) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium.
(d) Solve for the optimal allocation of leisure, l, the consumption, c, employment, N, output, Y . Contrast these quantities with those in competitive equilibrium from (2c). Is the competitive equilibrium identical to the optimal allocation? Explain why (not).
(e) Suppose that G increases. Discuss how the endogenous variables, {c, l, N, Y, w} change in competitive equilibrium.
(f) Suppose that z increases. Discuss how the endogenous variables, {c, l, N, Y, w} change in competitive equilibrium.
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