# Consider an open economy income-expenditure model of the economy where the country is in long-run equilibrium. Investment ( I ), government spending…

Consider an open economy income-expenditure model of the economy where the country is in long-run equilibrium.

•   Investment (I), government spending (G), and exports (X) are fixed: I = 300, G = 300, X = 200.

•   The income tax rate is t = 40%, so tax revenue equals T = tY .

•   Consumption is given by the consumption function C = 10 + 0.75Yd, where Yd = (1 − t)Y .

•   Finally, imports (M) are given by the import function M = 0.2Y .

(a)   Write down the aggregate expenditure function using the above values. What is the value of the intercept term? What is the value of the slope term? What is equilibrium output?

(b)   Plot the aggregate expenditure function on a chart, with output (Y ) on the horizontal axis, in increments of 200 from 0 to 2000.

(c)    In equilibrium, what is the trade balance? Is this a surplus or deficit? If this translates into the same surplus/deficit in the current account, what does this imply is happening to the country’s stock of net foreign debt?

(d)   What is the value of tax revenue, T? What is the value of government savings (T G). Is the government running a surplus or deficit?

(e)   Suppose the government wants to change spending; in particular it will set G so that it is equal the level of taxation you calculated in the previous question. After the government changes its level of expenditure, what is the new equilibrium level of output?

(f)     At the new level of equilibrium output, what is the new level of tax revenue? What is the new level of government savings? Is the surplus/deficit larger or smaller than it was in question? (d)?

(g)   Income-expenditure models keep both the price level and interest rates fixed.Discuss how allowing these to vary would have changed equilibrium output and the equilibrium tax take.