Consider the following Macro Economy i. Consumption Function: C 100 + 0.8 (Y-TA)

Question

Consider the following Macro Economy i. Consumption Function: C 100 + 0.8 (Y-TA) 11. Investment: I = 50 ii. Government Expenditure: G=100 v. Tax Function: TA = 0.25 Y ind out the government expenditure multiplier (ay) and goods market equilibrium with Y AD nd the new equilibrium level of output when government took a decision to increase its expenditure by 25 units but additionally decrease the tax rate by 0.05 Write about the following w changes in unemployment rate influences the growth of the economy using Okun's Law Write about Fisher's quantity theory of money Page 12

Explanation / Answer

a).

Consider the given problem here we have given all the required information.

So, at the equilibrium Y = AD, => Y = C + I + G = 100 + 0.8*(1 – 0.25)*Y + 50 + 100.

=> Y = (100 + 50 + 100) + 0.8*0.75*Y, => Y = 250 + 0.6*Y, => 0.4*Y = 250, => Y = 250/0.4 = 625.

=> Y = 625.

Now, let’s assume that at the equilibrium Y = AD, => Y = 100 + 0.8*(1 – 0.25)*Y + I + G.

=> dY = 0.8(1 – 0.2)*dY + dI + dG, here dG=25, dI=0.

=> dY = 0.64*dY + 25, => 0.36*dY = 25, => dY = 25/0.36 = 69.44.

=> if “G” increase by “25” and “tax rate” decreases by “0.05”, then the increase in “Y” is “dY=69.44”.

b).

As we know that “unemployment rate” and “output growth” is related to each other, => as “unemployment rate” increases, => comparatively less labor will be employed for production => less output will be produced, => there are negative relationship between “u” and “dY/Y=output growth”.

Now, “okun’s law” shows an empirical between “u” and “output growth”, => according to the law, if “unemployment” increases by “1%”, => then “output growth” will fall by “2%”.

Now, mathematically “g(Y) = c*(u – u0), where “c=(-2) and “u0 = natural rate of unemployment”.

c).

Now, “Quantity Theory of Money (QTM)”, shows a relationship between “M=money supply”, “V=Velocity of money”, “P=price level and T=total transaction.

So, mathematically, M*V = P*T, now to make the relationship more simple, we can replace “T” with “Y”.

=> M*V = P*Y, if we assume that “V” and “Y” is fixed, the above equation in growth form.

=> growth(M) + growth(V) = growth(Y) + growth(P), since “V” and “Y” is fixed, => growth(Y) = growth(V) = 0.

=> growth(M) = growth(P), => “QTM”, => growth of “M” is exactly equal to “P”, => if “M” increases by “1%”, => “P” will also increases by “1%”, => there is a positive relationship between “M” and “P”.

So, the “QTM” shows the one to one relationship between “M” and “P”, => if “M” increases by “1%”, => “P” also increases by “1%”.

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