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. 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. c. How does c∗ affect the slope of the IS curve? Explain your answer intuitively. 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

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.

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.

c. How does c∗ affect the slope of the IS curve? Explain your answer
intuitively.

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