based on supply of money

Question

given that money supply is ksh.1400millions,autonomous consumption is ksh.120 million, while the responsiveness of consumption to changes in disponsable income is estimated to be 80% by the ministry of planning.Aggregate autonomous investment is ksh.200 million investment while one 1% increase in interest rate changes investment by ksh.10 millions. The government collected ksh.200 million as tax revenue and wishes to increase expenditure by 10% above the revenue collected. The transactionary and precautionary demand for money function is expressed as m/p=0.1y while the speculative money demand m/p is =-100r.

[i] solve for equilibrium real output and equilibrium interest rate.

[ii] what is the effect of the new expenditure plan impact on income and consumption?

Answer 1

To solve this, we need to set up and solve the IS-LM model equations. Here’s how it breaks down:

(i) Solve for equilibrium real output and interest rate

1. IS Curve: Goods Market Equilibrium

The IS curve is given by:

Y=C+I+GY = C + I + GWhere:

1. C=a+c(Y−T)C = a + c(Y - T) is consumption, with a=120a = 120, c=0.8c = 0.8, and T=200T = 200,
2. I=I0−b⋅rI = I_0 - b \cdot r, with I0=200I_0 = 200 and b=10b = 10,
3. G=200G = 200, as government spending equals tax revenue initially.

Substitute CC, II, and GG into the IS equation:

Y=120+0.8(Y−200)+200−10r+200Y = 120 + 0.8(Y - 200) + 200 - 10r + 200Simplify:

Y=120+0.8Y−160+200−10r+200Y = 120 + 0.8Y - 160 + 200 - 10r + 200 Y=0.8Y+360−10rY = 0.8Y + 360 - 10rRearrange to isolate YY:

Y−0.8Y=360−10rY - 0.8Y = 360 - 10r 0.2Y=360−10r0.2Y = 360 - 10r Y=1800−50r(1: IS Curve)Y = 1800 - 50r \tag{1: IS Curve} 2. LM Curve: Money Market Equilibrium

The LM curve is given by:

MP=L(Y,r)\frac{M}{P} = L(Y, r)Where:

1. MP=1400\frac{M}{P} = 1400 (real money supply),
2. L(Y,r)=0.1Y−100rL(Y, r) = 0.1Y - 100r (money demand).

Set money supply equal to money demand:

1400=0.1Y−100r1400 = 0.1Y - 100rRearrange to isolate YY:

0.1Y=1400+100r0.1Y = 1400 + 100r Y=14000+1000r(2: LM Curve)Y = 14000 + 1000r \tag{2: LM Curve} 3. Solve IS and LM Simultaneously

From the IS curve:

Y=1800−50rY = 1800 - 50rFrom the LM curve:

Y=14000+1000rY = 14000 + 1000rSet the two equations equal to each other:

1800−50r=14000+1000r1800 - 50r = 14000 + 1000rSolve for rr:

1800−14000=1000r+50r1800 - 14000 = 1000r + 50r −12200=1050r-12200 = 1050r r=−11.62 %(Equilibrium Interest Rate)r = -11.62 \, \% \tag{Equilibrium Interest Rate}Substitute rr back into the IS curve to solve for YY:

Y=1800−50(−11.62)Y = 1800 - 50(-11.62) Y=1800+581Y = 1800 + 581 Y=2381 million KSh(Equilibrium Real Output)Y = 2381 \, \text{million KSh} \tag{Equilibrium Real Output} (ii) Effect of the New Expenditure Plan

New Government Expenditure

The government plans to increase spending by 10% above revenue collected. Since T=200T = 200, the new GG is:

Gnew=200+0.1(200)=220 million KShG_{\text{new}} = 200 + 0.1(200) = 220 \, \text{million KSh}New IS Curve

With the increased GG, the IS curve becomes:

Y=120+0.8(Y−200)+200−10r+220Y = 120 + 0.8(Y - 200) + 200 - 10r + 220Simplify:

Y=120+0.8Y−160+200−10r+220Y = 120 + 0.8Y - 160 + 200 - 10r + 220 Y=0.8Y+380−10rY = 0.8Y + 380 - 10rRearrange:

Y−0.8Y=380−10rY - 0.8Y = 380 - 10r 0.2Y=380−10r0.2Y = 380 - 10r Y=1900−50r(3: New IS Curve)Y = 1900 - 50r \tag{3: New IS Curve}New Equilibrium Output and Interest Rate

Solve the new IS and LM curves: From LM:

Y=14000+1000rY = 14000 + 1000rFrom the new IS curve:

Y=1900−50rY = 1900 - 50rSet the two equations equal:

1900−50r=14000+1000r1900 - 50r = 14000 + 1000rSolve for rr:

1900−14000=1000r+50r1900 - 14000 = 1000r + 50r −12100=1050r-12100 = 1050r r=−11.52 %(New Interest Rate)r = -11.52 \, \% \tag{New Interest Rate}Substitute rr into the new IS curve:

Y=1900−50(−11.52)Y = 1900 - 50(-11.52) Y=1900+576Y = 1900 + 576 Y=2476 million KSh(New Real Output)Y = 2476 \, \text{million KSh} \tag{New Real Output} Change in Income and Consumption

The increase in income is:

ΔY=2476−2381=95 million KSh\Delta Y = 2476 - 2381 = 95 \, \text{million KSh}Consumption is:

C=a+c(Y−T)C = a + c(Y - T)Before the change:

Cold=120+0.8(2381−200)=120+0.8(2181)=120+1744.8=1864.8C_{\text{old}} = 120 + 0.8(2381 - 200) = 120 + 0.8(2181) = 120 + 1744.8 = 1864.8After the change:

Cnew=120+0.8(2476−200)=120+0.8(2276)=120+1820.8=1940.8C_{\text{new}} = 120 + 0.8(2476 - 200) = 120 + 0.8(2276) = 120 + 1820.8 = 1940.8The increase in consumption is:

ΔC=1940.8−1864.8=76 million KSh\Delta C = 1940.8 - 1864.8 = 76 \, \text{million KSh} Final Results:

1. Initial Equilibrium:
2. Output (YY): 2381 million KSh
3. Interest rate (RR): -11.62%
4. New Equilibrium (after government spending increase):
5. Output (YY): 2476 million KSh
6. Interest rate (RR): -11.52%
7. Impact of New Expenditure Plan:
8. Change in income (ΔY\Delta Y): +95 million KSh
9. Change in consumption (ΔC\Delta C): +76 million KSh