In the Keynesian cross, assume the following equation gives the consumption function.𝐶 ൌ 200 ൅ 0.75ሺ𝑌 െ 𝑇ሻPlanned investment is 100, and 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 to 125, what is the new equilibrium income?(d) What level of government purchases is needed to achieve an income of 1,600?

(a) To graph planned expenditure as a function of income, we first need to find the equation for planned expenditure. In the Keynesian cross model, planned expenditure (PE) is the sum of consumption (C), planned investment (I), and government purchases (G).

Given the consumption function C = 200 + 0.75(Y - T), planned investment I = 100, and government purchases G = taxes T = 100, we can substitute these values into the equation to get:

PE = C + I + G PE = [200 + 0.75(Y - 100)] + 100 + 100 PE = 200 + 0.75Y - 75 + 200 PE = 0.75Y + 325

This equation represents a line with a slope of 0.75 (the marginal propensity to consume) and a y-intercept of 325 (autonomous spending).

(b) The equilibrium level of income is found where planned expenditure equals income, or PE = Y. Setting the equations equal to each other, we get:

0.75Y + 325 = Y 325 = 0.25Y Y = 1300

So, the equilibrium level of income is 1300.

(c) If government purchases increase to 125, the new equation for planned expenditure becomes:

PE = 0.75Y + 350

Setting PE = Y to find the new equilibrium income, we get:

0.75Y + 350 = Y 350 = 0.25Y Y = 1400

So, the new equilibrium income is 1400.

(d) To achieve an income of 1600, we need to find the level of government purchases that makes PE = Y. Setting the equations equal to each other, we get:

0.75Y + G = Y G = 0.25Y G = 0.25 * 1600 G = 400

So, government purchases of 400 are needed to achieve an income of 1600.