Case Scenario:
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
1. 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)
2. 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
3. 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.
4. 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