Question

In the Keynesian cross model, assume that the consumption function is given by C=200+0.75*(Y-T) Planned investment is 100; government purchases and taxes are both 100.

a) Graph planned expenditure as a function of income. You should be able to have specific Numbers for your intercepts since you are given specific functional forms)

b) What is the equilibrium level of income?

c) If government purchases increase to 125, what is the new equilibrium income? What is the multiplier for government purchases?

d) What level of government purchases is needed to achieve an income of 1,600? (taxes remain at 100.)

(Hint : an income increase to 1,600 represents an increase of "..." over the original value of income. Use the government purchases multiplier formula and this "..." increase to calculate by how much must government purchases change to get this "..." increase in income)​

Answer 1

Step-by-step explanation:

a) To graph planned expenditure as a function of income, we need to use the Keynesian cross model. In this model, the planned expenditure (E) is equal to the sum of consumption (C) and planned investment (I), and is represented by the equation E = C + I. Given the consumption function C = 200 + 0.75*(Y - T) with T = 100 and I = 100, we can write the planned expenditure function as follows:

E = C + I

E = (200 + 0.75*(Y - 100)) + 100

E = 300 + 0.75Y - 75

E = 225 + 0.75Y

To graph this function, we plot E on the vertical axis and Y on the horizontal axis. The intercept on the vertical axis is 225, and the slope of the line is 0.75. The graph is a line that starts at the point (0, 225) and has a slope of 0.75.

b) To find the equilibrium level of income, we need to set planned expenditure equal to actual expenditure, which is equal to income (Y) in the Keynesian cross model. Thus, we have:

Y = E

Y = 225 + 0.75*Y

Solving for Y, we get:

Y = 900

Therefore, the equilibrium level of income is 900.

c) If government purchases increase to 125, the new planned expenditure function becomes:

E = C + I + G

E = (200 + 0.75*(Y - 100)) + 100 + 125

E = 425 + 0.75*Y

To find the new equilibrium income, we set planned expenditure equal to income (Y) again:

Y = E

Y = 425 + 0.75*Y

Solving for Y, we get:

Y = 1,300

Therefore, the new equilibrium income is 1,300. The multiplier for government purchases is given by:

Multiplier = 1/(1 - MPC)

where MPC is the marginal propensity to consume. In this case, MPC = 0.75, so the multiplier is:

Multiplier = 1/(1 - 0.75) = 4

d) To find the level of government purchases needed to achieve an income of 1,600, we need to use the government purchases multiplier formula:

Change in Y = Multiplier * Change in G

The "..." increase in income is 1,600 - 900 = 700. We want to know by how much government purchases must change to get this increase in income. We can rearrange the formula to solve for the change in government purchases:

Change in G = Change in Y / Multiplier

Change in G = 700 / 4

Change in G = 175

Therefore, the level of government purchases needed to achieve an income of 1,600 is 100 + 175 = 275. Taxes remain at 100 in this case.