Question

In Sufrolandia the consumption function is C = 180 + 0.8(Y − T). The government collects direct and indirect taxes according to T = 100 + 0.5 ∗ Y . Unfortunately, the tax revenue is not enough to cover the public expenditure.MadreM´ıa, a firm formed by prominent IE graduates, has been hired to design a policy that reduces the deficit. However, they recommend to increase public spending by 300 million, rather than cutting spending and raising taxes! They argue that since c 0 = 0.8 the multiplier is very high, thus the high multiplier, together with the combination of a high tax rate on income (50% !!), will make the tax collection more than sufficient to finance the increase in government spending. Your friends convince D. Trump (the dictator) and they increase G. Should the IE graduates be thrown to jail because the policy failed to decrease the budget deficit?. Proceed as follows: first, calculate the INCREASE in GDP (you do not have sufficient data to calculate the level of GDP, but you have enough data to calculate the NEW government spending multiplier. —if you cannot find the multiplier, read the note at the end of this problem set—). Then calculate by how much government revenue increases. Does the government deficit increases or decreases? That is, should Mr. Trump send to jail to your buddies or regard them as national heroes?

Answer #1

Consider the given problem here the consumption function is, “C=180+0.8*(Y-T)”, where “MPC=0.8”. So, here the government spending multiplier is given by.

=> dY/dG = 1/[2-MPC*(1-t)], where “MPC=0.8” and “t=income tax rate=0.5”.

=> dY/dG = 1/[1-MPC*(1-t)], => dY/dG = 1/[1-0.8*(1-0.5)] = 1/[1-0.8*0.5] = 1/[1-0.4] = 1/0.6.

=> dY = dG/0.6 = 300/0.6 = 500, => dY = 500 > 0.

So, as the public spending increases by “dG=$300”, the GDP also increases by “dY=$500”. Now, the tax function is given by, => T = 100 + 0.5*Y, => dT = 0.5*dY, => dT = 0.5*500 = 250, => dT = 250 < dG.

Here as the public spending increases by $300 that increases the tax revenue by $250, => budget deficit increases, => the increase in public spending fails to increase budget deficit.

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