Consider the following economy: Aggregate Expenditure = + + + Consumption = + ( ) Investment = Taxes = Inflation = 1 + e + Government Expenditure and Trade = , = , = In this economy, taxes depend on the level of income. Moreover, consumption depends on disposable income (income net of taxes) and not just on the level of income as we assumed in class. Use the previous equations to answer the following

questions: 1

(a) (4 points) Solve for the equilibrium in the goods market. What is the expenditure multiplier?

(b) (7 points) Use the Keynesian Cross to carefully explain the effect of a positive shock to the government expenditure, , for two cases: i. < 1, ii. = 1 (carefully label both graphs, including the slope of the expenditure function). What is the assumption we need to make to guarantee an equilibrium exists?

(c) (4 points) Derive the IS curve using deviations from potential output as the endogenous variable. (d) (9 points) Suppose the economy is at its potential output equilibrium with a constant 2% inflation rate. Using the full short-run model (IS-MP and Phillips curve), explain what happens to the economy over time if the government decides to increase the level of expenditure for two periods. Be sure to include graphs showing how deviations from potential output and inflation respond over time. Assume that < 1.

If we assume that the government budget is balanced when output is at its potential level (i.e. e = 0), we can write the fiscal surplus that results from government expenditure changes as follows ( < 0 is a deficit): = ( ) ( ) (e) (4 points) Solve for government budget surplus as a function of , , and the multiplier [Hint: The only difference between and , is that is a function of and is a function of ] .

(f) (7 points) Using graphs showing how the government fiscal surplus responds over time, analyze how the shock in part affects the government budget.