Question

This problem asks you to analyze the IS-LM model algebraically. First the consumption function and investment function from the goods market will be examined. Then, the money demand function from the money market will be examined. The Goods Market: Suppose consumption is a linear function of disposable income: C(Y- Ta bY - T), where a >0 and 0< b< 1. The parameter b is the marginal propensity to consume. The parameter a is a constant, often called autonomous consumption. Suppose also that investment is a linear function of the interest rate: I(r)-c - dr, where c0 and d>0. The parameter d measures the sensitivity of investment to the interest rate. The parameter c is a constant, often called autonomous investment. a. Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d. How does the slope of the IS curve depend on the parameter d, the interest sensitivity of investment? b. The higher the value of d, the the IS curve. Which would have more impact on equilibrium Y: a S100 increase in government purchases or a $100 tax cut? c. A $100 will create bigger horizontal shift in the IS curve. The money market: Now suppose demand for real money balances is a linear function of income (Y) and the interest rate (r): Lr, - eY -fr, where: e>0 and f> 0. The parameter e measures the sensitivity of money demand to Y, while the parameter fmeasures the sensitivity of money demand to r. d. Solve for r as a function of Y, M, and P and the parameters e and f. Answer units How does the slope of the LM curve depend on the parameter f, the sensitivity of money demand tor?

Need help, please show work

Blank options for B, E, and F are either 'steeper or flatter."

Blank options for C are "decreases in taxes or increase in govt purchases."

Answer 1

AS PER HOMEWORKLIB POLICY ANSWER IS SOLVED

A ] Y= C + L +G

C [ Y-T ] = A + B [ Y - T ]

I [ R ] = C - D R

Y = A - B [ Y - T ] + C - DR + G

Y = BY - DR + A + C +G - BT

Y = [ A + C G - BT ] / 1 - B ] - DR /[ 1- B ]

B ] IN THIS IS CURVE WE PLOT Y ARE R HIGHER THE D FLATTER THE IS CURVE WOULD BE VICE VERSIA

C ]WE SEE THAT THE MULTIPLIER FOR G IS 1 / 1- B

WHERE FOR T IS - B / 1- B

B < 1 WE KNOW THAT THE MULTIPLIER FOR G IS GREATER THIS MEANS THAT THE $100 INCRESES IN GOVT SPENDING WILL HAVE A LARGER IMPACT THAN THE $100 TAX CUT

TAX CUTS LEADS TO INCREASES IN DISPOSABLE INCOME OF PEOPLE BUT SOME TIMES OF THEB INCREASES INCOME GOES TO SAVINGS AND THE NET INCREASES IN CONSUMPTION IS SMALLER

D REAL MONEY DEMAND L [ R , Y ] = E Y - FR

REAL MONEY SUPPLY = M /P

WHERE M IS NORMAL MONEY SUPPLY

P IS THE PRICE

AT EQUILI BRUIM IN MONEY DEMAND S = MONEY SUPPLY  

EY - FR = M / P

R = [ EY - [M / P ] / F

E ] THE LM WILL BE STEEPER FOR SMALL F VICE VERSA

THE SLOPE OF THE CURVE = E / F WHICH IS LARGER FOR SMALL F

THE INTUTION BEHIND IS THAT THE MONEY DEMANDS IS HIGHLY SENSITIVE TO R THAN A SMALL DECREASES

IN R WOULD HAVE TO BE COMPANSATED BY A VERY HIGH INCREASES IN Y IF THE REAL MONEY SUPPLY REMAINS CONSTANT