Question

C = 50 + 0.8YD 

I = 70 

G = 200 

TR = 200 (i.e. Transfer Payments) 

t = 0.20 

(a) Calculate the value of multiplier and equilibrium level of GDP. 

(b) Calculate the Budget Surplus. 

(c) Suppose that tax rate increases from 20% to 25%, what is the new equilibrium 

income? What is the new multiplier? Also calculate the change in budget surplus. 

(d) Would you expect the change in the surplus to be more or less if the value of MPC 

had been 0.9 rather than 0.8? 

(e) Can you explain why the value of multiplier is 1 when t = 1.

Answer 1

$$\\$$ $$Solution$$

[A]

$AE = C + I + G = 50 + 0.8YD + 70 + 200 = 320 + 0.8(Y – T + TR)\\ AE = 320 + 0.8(Y − 0.2Y + 100) = 350 + 0.8(0.8Y + 100)\\ AE = 320 + 0.64Y + 80 and finally AE = 400 + 0.64Y\\ Then\ set\ it \ equal\ to\ Y\ in\ order\ to\ find\ the\ equilibrium\ level\ of\ income\ :\\ Y = AE = 400 + 0.64Y\ and\ 0.36Y = 400 \ and\ Y_e = (1/0.36)400 = 1111.1\\ The\ closed \ economy\ multiplier\ (αG)\ is\ (1/0.36) = 2.778\\$

[B]$BS = T – TR – G = 0.2(1111.1) – 100 – 200 = 222.2 – 300 = −77.8 (deficit) .$

[C]

$When\ t = 0.25,\\ AE = C + I + G = 50 + 0.8YD + 70 + 200 = 320 + 0.8(Y – T + TR)\\ AE = 320 + 0.8(Y − 0.25Y + 100) = 350 + 0.8(0.75Y + 100)\\ AE = 320 + 0.6Y + 80 \ and\ finally\ AE = 400 + 0.6Y\\ Then\ set\ it\ equal\ to\ Y\ in\ order\ to\ find \ the\ equilibrium\ level\ of\ income:\\ Y = AE = 400 + 0.6Y and 0.4Y = 400 and Ye = (1/0.4)400 = 1000\\ The\ closed \ economy\ multiplier\ (αG)\ is\ (1/0.4) = 2.5\\$

$The \ new\ BS = T – TR – G = 0.25(1000) – 100 – 200 = 250 – 300 = −50\\ Deficit \ get\ smaller\ due \ to \ increase\ in\ tax\ rates\ even\ though\ the\\ income\ level\ drops\ as\ well.$

[D]

Yes . The higher the MPC, the higher the multiplier—the more the increase  in consumption from the increase in investment. there will be change in business surplus hence in this case (reduction in budget deficit )to be smaller if MPC was higher since then the impact of tax rate change in multiplier will be less due to the formula of multiplier.

[E]

If you look at the multiplier formula$(1/(1-c(1-t)),$ if the tax rate is $1,$ then $(1 − t)$ will be zero and c$(1 − t)$ will also be zero. Then the multiplier formula will be $1/1 = 1$ . If the tax rate is one hundred percent, that is one every rise in autonomous spending will raise people's income by the same amount, but this increase in income will be swiftly collected as tax by the government. As a result, people will have no extra money to spend. As a result, the multiplier process will fail completely.