Question

USU.US CUJL 1.ULTIUZULUV.CUIT 1. Points = 18 Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 0<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars f> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If we know the parameters of the system, find the numerical value of the equilibrium GDP (Y) as well as the equilibrium levels of C, I, and T (3 points); Parameters' values are as follows: a = 10; b = 0.7; f= 3; j = 0.2, k = 25; r = 0.03. Endogenous Government Expenditure is Go = 55. 4) Find the government-expenditure multiplier and discuss its economic meaning (3 points); 5) Find the non-income tax multiplier and discuss its economic meaning (3 points); 6) Find the extent to which an increase in the income tax rate (j) will affect the equilibrium income Y (3 points).

Answer 1

1).

Here “C” be the aggregate consumption of the economy as a whole, which is positively related to the disposable income. So, as the “disposable income” increases the “aggregate consumption of the economy” also increases. Now, “I” be the aggregate investment of the economy, measure the total investment of the economy as whole, which is positively related to the overall income. So, as the “overall income” increases the “aggregate investment of the economy” increases.

Now, “G” be the government’s expenditure measure the “government investment” in different public projects, “government’s spending” on goods and services and the transfer payments. “T” be the overall tax of the economy as whole, which is also positively related to the “overall income of the economy as whole”.

Now, the overall income of the economy is sum of total expenditure of the economy as whole. So, at the equilibrium “Y” must be equal to sum of “C”, “I”, and “G”.

2).

Here the equilibrium condition is given by.

=> Y = C+I+G, => Y = [a + b*(Y-T)] + [k + r*Y] + G0, => (1-r)*Y = a + b*Y - b*T + k + G0, => (1-r-b)*Y = a - b*T + k + G0.

=> (1-r-b)*Y = a - b*(f + j*Y) + k + G0, => (1-r-b)*Y = a - b*f - j*Y + k + G0, => (1-r-b+j)*Y = a - b*f + k + G0.

=> Y = [a - b*f + k + G0]/ (1-r-b+j), be the equilibrium level of economy of the given economy.

3).

Let’s assume that “a=10”, “b=0.7”, “f=3”, “j=0.2”, “k=25”, “r=0.03” and “G0=55”.

=> Y = [a - b*f + k + G0]/ (1-r-b+j), => Y = [10 – 0.7*3 + 25 + 55]/ (1-0.03-0.7+0.2).

=> Y = 87.9/ 0.47 = 187.02, => Y = 187.02.

4).

Here the equilibrium income is given below.

=> Y = [a - b*f + k + G0]/ (1-r-b+j), let’s assume “G” increase by “dG” units and other things remains same.

=> dY = dG0/ (1-r-b+j), => dY/dG0 = 1/(1-r-b+j) = government spending multiplier.

Now, for the given values of the parameters the numerical value is given below.

=> dY/dG0 = 1/(1-r-b+j), => dY/dG0 = 1/(1-0.03-0.7+0.2) = 1/0.47 = 2.13 > 0. So, here the multiplier shows how much the equilibrium income will change as the “G” increases by “1 units”. So, here the multiplier value is “2.13” implied if “G” increases by “1 units” the equilibrium income also increases by “2.13 units”.