# Multiplier accelerator interaction

Consider a macro model that has both a consumption function that depends on lagged income (Like Freidman's permanent income equation) and an investment equation that depends with a lag, on changes in income. Ignore interest - rate effects. In particular assume that the following equations describe the economy

Y= C+I+G

C= 220+ 0.63Yp with Yp =0.5(Y+ Y-1 )

I= 900 + 0.2(Y-1 - Y-2)

G= 1200

A. By algebraic substitution of Can I into the income identity, obtain a single expression for both output Y in terms of output in the previous years (Y-1 and Y-2)

B. Calculate the constant level of output Y that satisfies all the relationships in the model (Hint set Y -1 =Y and Y -2 =Y in the equation from part a and solve for Y using algebra

C. Suppose that y is = to the value you calculated in part b for the past 2 years (Years 1 and 2) Now suppose that government spending increases by $50 billion in year 3 calculate the effect on output in year 3 . Calculate the effect on output in years 4 through 10 . Be sure to use the relationship you derived in part a and substitute the values for Y -1 and Y -2 you calculated in the previous two steps.

D. Plot the values of Y on a diagram with the years on the horizontal axis. Do you notice any cyclical behavior in Y. Explain what is going on ( this model was originally developed by Paul Samuelsson of M.I.T) while a student at Harvard in the 1930's

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