1. (40 Points) Consider the intertemporal model of consumer choice with real investment developed in class. Consumers make choices on labour/leisure, consumption across periods, and savings. Firms make labour and investment decisions. The government has an exogenous amount of expenditures in each period and finances these with lump- sum taxes on consumers. The economy is initially in equilibrium.

(a)(10 Points) Assume the firm's production functions are described byY=zKN1andY=z(K)(N)1. Derive the investment demanded by the firm, givenw,N,K, andr. Show how the firm's demand for investment changes if the govern- ment imposes a proportional taxon the firm's operating profits (current and future), where operating profits are defined as total revenue (including from any future capital sold) minus wage costs. Use a graph to show the firm's investment demand curve with and without this tax.

(b)(15 Points) Suppose there is an increase in current government expendituresG, but that these expenditures are used to supply public goods (free to use) that consumers value. Imagine consumers value these public goods so much that they perceive their utility as increasing (for any given quantity of labor supplied), so there is a positive income effect on labor decisions. Explaining each step, show using two graphs how it is possible for employment to remain unchanged as a result of this increase inG. What happens to the current wage, the interest rate, and current output as a result?

(c)(15 Points) Illustrate using two graphs how news about a future decrease in TFP will affect current employment, the current wage, current output, and the interest rate. Explain each step.