Question

Solve 1. 2. 3. 4. 5.

1 Keynesian Cross Assume that households' consumption function is given by C(Y -T) 50+ 0.75(Y T), that firms' investment function is I(r) 150 10r, government spending is G 150, and the tax bill T 200. 1. What is the Marginal Propensity to Consume "MPC")? 2. What is the equilibrium level of real GDP in the goods market if the real interest rate is 5%? (Plug in r = 5 for 5%, rather than 0.05 This is an assumption about the way we scale the coefficients in the investment function.) 3. Plot the Keynesian Cross, showing planned expenditure and the equilib rium lines. 4. Suppose government spending increases to 200 and taxes remain constant. How much does GDP rise, holding constant the interest rate. What is the government spending multiplier? How do the lines from the previous graph shift? 5. Suppose taxes also rise by 50 to compensate for the increase in spending. What is the new level of GDP? Is it higher or lower than the one before government spending and taxes both rose?

Answer 1

C(Y - T) = 50 + 0.75 (Y -T)

I(r) = 150 - 10r

G = 150

T = 200

1. Here, from the consumption equation, we see that Marginal Propensity to consume is 0.75.

2. We know, Y = C + I + G

= 50 + 0.75 (Y -T) + 150 - 10r + 150

Putting r =5 and T =200

Y = 50 + 0.75Y - 0.75(200) + 150 -10(5) + 150

0.25Y = 50 - 150 +150 - 50 +150

0.25Y = 150

Y = 150/ 0.25 = 600

3.

5 0 6 oo 900

The intersection of the Planned expenditure and the 45⁰ line shows the equilibrium Output.

4. If the government spending increases (G') to 200, and taxes remain constant.

0.25Y = 50 - 150 +150 - 50 +200

0.25Y = 200

Y = 800

GDP rises 200 units.

Government spending multiplier = $\Delta Y/\Delta G$ = (800 - 600)/ (200 - 150) = 200/ 50 = 4

The lines from the previous graph shift upward showing the increase in government spending.

5. Now, taxes also increase by 50.

Y = 50 + 0.75 (Y -T) + 150 - 10r + 200

0.25Y = 50 - 0.75(250) +150 - 10(5) + 200

0.25Y = 50 - 187.5 + 150 - 50 + 200

0.25Y = 162.5

Y = 650

It is higher than the one before the government spending and taxes rose. Earlier it was 600.