Assume That the Consumption Function Is Given by C = $I S$

Essay

Assume that the consumption function is given by C = 200 + 0.5(Y - T) and the investment function is I = 1,000 - 200r, where r is measured in percent, G equals 300, and T equals 200. a. What is the numerical formula for the $I S$ curve? (Hint: Substitute for $C , I$ , and $G$ in the equation $Y = C + I + G$ and then write an equation for $Y$ as a function of $r$ or $r$ as a function of $Y$ .) Express the equation two ways.
b. What is the slope of the IS curve? (Hint: The slope of the IS curve is the coefficient of $Y$ when the IS curve is written expressing $r$ as a function of $Y$ .)
c. If $r$ is one percent, what is $I$ ? What is $Y$ ? If $r$ is 3 percent, what is $I$ ? What is $Y$ ? If $r$ is 5 percent, what is $I$ ? What is $Y$ ?
d. If $G$ increases, does the $I S$ curve shift upward and to the right or downward and to the left?