I already have A,B,C and i have posted the answers with this. Can i please just get help with D,E,F? I would very much appreciate it.Please. Consider the Aggregate expenditure model. Where: AD = C + I + G + NX where G, and NX are all autonomous. C = C + c∗(Y + T R − T A) where T A = tY with t ∈ [0, 1] is the proportional tax rate and c ∗ ∈ (0, 1) is the marginal propensity to consume. In addition, investment is given by: I = I − bi where I is autonomous investment and b > 0 determines the sensitivity of investment to changes in the interest rate, i. A. Using the information above, solve for the IS function. Combine all the autonomous terms into one term, A. (a) AD = C + I + G + NX---------(I) C = C + c∗(Y + T R − T A)-------(II) TA=tY ------(III) I-I-bi-----(IV) The equilibrium for IS curve is at the point where; Planned output f(Y,i)= Actual planned output f(Y*,i*) Y=AD Putting (I) in the above equation =C + I + G + NX Putting (II) and (III) in the above equation =C + c∗(Y + T R − T A)+(I-bi) + G + NX Putting (IV) in the above equation =C + c∗(Y + T R − tY)+(I-bi) + G + NX Now, all the autonomus terms are taken together Y=(C + I + G + NX)+c*TR-bi-c*tY+c*Y Let A=(C + I + G + NX)++c*TR The IS function is Y=A-bi-c*tY+c*Y B. In an (x, y) plane, where Y is on the horizontal axis and i is on the vertical axis, illustrate the IS curve you derived above. Make sure to explain how you got the Y-intercept and solve for the slope. (b) The IS curve is derived by plotting all the interest rates (i) and the planned level of output (Y). To plot the IS curve on the graph we first need to determine the slope of the curve. IS Curve function: Y=A-bi-c*tY+c*Y Y= A-bi-c*(t-1)The above equation can be re-written asY= A-bi+c*(t-1)Let 11-c*(t-1)=αGY=αG A-biDerivating both sides to find slopedidy=αG(0-b)Slope=-αGbSince, the slope is negativeThe IS curve is downard sloping c. How does c∗ affect the slope of the IS curve? Explain your answer intuitively. (c) c* i.e., the autonomus consumption has a direct impact on determining the IS curve. Any change in the c* will shift the IS curve either inward or outward. If the c* increases the IS curve shifts outward and if the c* decreases then the IS curve shifts inward. c* changes the αg. The smaller the amount of αg the steeper the IS curve is. αg is composed of 1/1-c*(1-t). C* is in the denominator so any increase in c* will increase the denominator which reduces αg. A decrease in αg will make the IS curve slope steeper. d. Consider the LM curve, where the real demand for money is such that: MD/P= kY − hi where k ∈ (0, 1) represents how sensitive the demand for money is to changes in income (or the inverse of the velocity of money). Moreover, h > 0 indicated the sensitivity of real money demand for interest rates (the opportunity cost of holding money). The price level, P is constant. Finally, the money supply is under total control of the monetary authority and is given by: M*/P. Impose equilibrium in the money market and solve for the LM curve. e. In an (x, y) plane, where Y is on the horizontal axis and i is on the vertical axis, illustrate the LM curve you derived above f. Graphically, illustrate the equilibrium in the goods and money markets, where IS = LM. Show graphically what happens to the equilibrium levels of output and real interest rates when the money supply decreases. Explain your answer by highlighting the transmission channels.
I already have A,B,C and i have posted the answers with this. Can i please just get help with D,E,F? I would very much appreciate it.Please.
Consider the Aggregate expenditure model. Where:
AD = C + I + G + NX
where G, and NX are all autonomous.
C = C + c∗(Y + T R − T A)
where T A = tY with t ∈ [0, 1] is the proportional tax rate and c
∗ ∈ (0, 1) is the marginal propensity to consume. In addition, investment is given by: I = I − bi
where I is autonomous investment and b > 0 determines the sensitivity of
investment to changes in the interest rate, i.
A. Using the information above, solve for the IS function. Combine all the autonomous terms into one term, A.
(a) AD = C + I + G + NX---------(I)
C = C + c∗(Y + T R − T A)-------(II)
TA=tY ------(III)
I-I-bi-----(IV)
The equilibrium for IS curve is at the point where;
Planned output f(Y,i)= Actual planned output f(Y*,i*)
Y=AD
Putting (I) in the above equation
=C + I + G + NX
Putting (II) and (III) in the above equation
=C + c∗(Y + T R − T A)+(I-bi) + G + NX
Putting (IV) in the above equation
=C + c∗(Y + T R − tY)+(I-bi) + G + NX
Now, all the autonomus terms are taken together
Y=(C + I + G + NX)+c*TR-bi-c*tY+c*Y
Let A=(C + I + G + NX)++c*TR
The IS function is
Y=A-bi-c*tY+c*Y
B. In an (x, y) plane, where Y is on the horizontal axis and i is on the
vertical axis, illustrate the IS curve you derived above. Make sure to explain
how you got the Y-intercept and solve for the slope.
(b) The IS curve is derived by plotting all the interest rates (i) and the planned level of output (Y). To plot the IS curve on the graph we first need to determine the slope of the curve.
IS Curve function: Y=A-bi-c*tY+c*Y Y= A-bi-c*(t-1)The above equation can be re-written asY= A-bi+c*(t-1)Let 11-c*(t-1)=αGY=αG A-biDerivating both sides to find slopedidy=αG(0-b)Slope=-αGbSince, the slope is negativeThe IS curve is downard sloping
c. How does c∗ affect the slope of the IS curve? Explain your answer
intuitively.
(c) c* i.e., the autonomus consumption has a direct impact on determining the IS curve. Any change in the c* will shift the IS curve either inward or outward. If the c* increases the IS curve shifts outward and if the c* decreases then the IS curve shifts inward.
c* changes the αg. The smaller the amount of αg the steeper the IS curve is. αg is composed of 1/1-c*(1-t). C* is in the denominator so any increase in c* will increase the denominator which reduces αg. A decrease in αg will make the IS curve slope steeper.
d. Consider the LM curve, where the real demand for money is such that:
MD/P= kY − hi
where k ∈ (0, 1) represents how sensitive the demand for money is to changes
in income (or the inverse of the velocity of money). Moreover, h > 0 indicated
the sensitivity of real money demand for interest rates (the
holding money). The price level, P is constant. Finally, the money supply is
under total control of the monetary authority and is given by:
M*/P.
Impose equilibrium in the
e. In an (x, y) plane, where Y is on the horizontal axis and i is on the vertical
axis, illustrate the LM curve you derived above
f. Graphically, illustrate the equilibrium in the goods and money markets,
where IS = LM. Show graphically what happens to the equilibrium levels of
output and real interest rates when the money supply decreases. Explain your
answer by highlighting the transmission channels.
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