Suppose the economy consists of a representative agent with the following utility function: P U = Cα ( M )1−α. Labor is supplied exogenously at level L¯. Output is sup- plied by a perfectly competitive representative firm, which has production function Y = Lη . Any profits are remitted to the representative agent. There is a government, which purchases amount G of goods and services. This amount is financed by a lump-sum tax, of level T and seigniorage. Money is the only asset in the economy; initial money holdings are given by M l. Money is supplied exogenously by the government. Assume both prices and wages are flexible. (a) Write down the consumer’s and the firm’s intertemporal maximiza- tion problems. (b) Solve for expressions for aggregate demand and supply (that is, out- put as a function of the price level) and for the equilibrium price and wage levels as a function of exogenous variables. (c) Describe the effects of increases in initial money holdings M l on all the endogenous variables in this economy. (d) Describe the effects of increases in government purchases G on all the endogenous variables in this economy. Now assume that the nominal wage is permanently fixed at W = W¯ . In solving the problems below, you may make further convenient assumptions about the level of W¯ , with justification. (e) Solve for expressions for aggregate demand and supply (that is, out- put as a function of the price level). (f) Solve for the level of unemployment, if applicable. (g) Describe the effects of increases in initial money holdings M l on all the endogenous variables in this economy. (h) Would your answers to the previous parts qualitatively change if the price level were fixed instead of the nominal wage level?
5. Suppose the economy consists of a representative agent with the following utility function:
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by M l. Money is supplied exogenously by the government.
Assume both prices and wages are flexible.
(a) Write down the consumer’s and the firm’s intertemporal maximiza- tion problems.
(b) Solve for expressions for aggregate
(c) Describe the effects of increases in initial money holdings M l on all the endogenous variables in this economy.
(d) Describe the effects of increases in government purchases G on all the endogenous variables in this economy.
Now assume that the nominal wage is permanently fixed at W = W¯ . In solving the problems below, you may make further convenient assumptions about the level of W¯ , with justification.
(e) Solve for expressions for aggregate demand and supply (that is, out- put as a function of the price level).
(f) Solve for the level of
(g) Describe the effects of increases in initial money holdings M l on all the endogenous variables in this economy.
(h) Would your answers to the previous parts qualitatively change if the price level were
fixed instead of the nominal wage level?
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