2. In the Keynesian cross , assume that the consumption function is given by C=200+0.75(Y-T) Planned investment is100:government purchases and taxes are both 100. A. Graph planned expenditure as a function of income. B. What is the equilibrium level of income? C. If government purchases increase to125, what is the new equilibrium income? D. What level of government purchases is needed to achieve an income of 1,600 ?

##Step 1: Setting up the Keynesian Cross Equation<br />###The Keynesian cross equation states: $Y = PE = C + I + G$, where Y is income, PE is planned expenditure, C is consumption, I is investment, and G is government purchases. We are given $C = 200 + 0.75(Y - T)$, $I = 100$, $G = 100$, and $T = 100$. Substituting these values into the Keynesian cross equation, we get: $Y = 200 + 0.75(Y - 100) + 100 + 100$.<br /><br />##Step 2: Solving for Equilibrium Income (Part B)<br />###Simplifying the equation from Step 1: $Y = 200 + 0.75Y - 75 + 100 + 100$, which becomes $0.25Y = 325$. Solving for Y, we get $Y = \frac{325}{0.25} = 1300$.<br /><br />##Step 3: New Equilibrium Income with Increased Government Purchases (Part C)<br />###With $G$ increasing to 125, the equation becomes $Y = 200 + 0.75(Y - 100) + 100 + 125$. Simplifying, we get $0.25Y = 350$, so $Y = \frac{350}{0.25} = 1400$.<br /><br />##Step 4: Government Purchases for a Target Income (Part D)<br />###We want to find G such that $Y = 1600$. The equation is $1600 = 200 + 0.75(1600 - 100) + 100 + G$. Simplifying, we get $1600 = 1325 + G$, so $G = 1600 - 1325 = 275$.<br /><br />##Step 5: Graphing Planned Expenditure (Part A)<br />###The planned expenditure function is $PE = 200 + 0.75(Y - 100) + 100 + 100 = 325 + 0.75Y$. This is a linear equation with an intercept of 325 and a slope of 0.75. The equilibrium is where this line intersects the $Y = PE$ line (or the 45-degree line).<br /><br /><br />#