Assume the Following Model of the Economy, with the Price

Essay

Assume the following model of the economy, with the price level fixed at 1.0: $$\begin{array} { l l } C = 0.8 ( Y - T ) & T = 1,000 \\I = 800 - 20 r & G = 1,000 \\Y = C + I + G & M / P = M / P = 0.4 Y - 40 r \\M = 1,200 &\end{array}$$ a. Write a numerical formul a for the $I S$ curve, showing $Y$ as a function of $r$ alone. (Hint: Substitute out $C , L , G$ , and $T$ .)
b. Write a numerical formula for the $L M$ curve, showing $Y$ as a function of $r$ alone. (Hint: Substitute out $M A P$ .)
c. What are the short-tun equilibrium values of $Y , r , Y - T , C , I$ , private saving, public saving, and nati onal saving? Check by ensuring that $C + I + G = Y$ and national saving equals $l$ .
d. Assume that $G$ increases by 200 . By how much will $Y$ increase in short-tun equilibrium? What is the government-purchases multiplier (the change in $Y$ divided by the change in $G$ )?
e. Assume that $G$ is back at its original level of 1,000 , but $M M ^ { 5 }$ (the money supply) increases by 200. By how much will $Y$ increase in short-run equilibrium? What is the multiplier for money supply (the change in $Y$ divided by the change in $M F$ )?