C = 100 + .5 Y D I = 100 + .1 Y – 500 i G = 100 T = .2 Y The public holds one-th

Question

C = 100 + .5 YD

I = 100 + .1 Y – 500 i

G = 100

T = .2 Y

The public holds one-third of its money in currency (c = 1/3) and two-thirds of its money in checkable deposits. Banks hold one-quarter of deposits in reserves ( =1/4). High powered money, Hs, is 50, the demand for real balances is

                                                            Md/P = Y – 4000 i

and the price level, P, is initially 1.

a) The IS relation.

a. Calculate the IS relation for this economy. [Put Y on one side of the IS equation and

everything else on the other side of the equation.]

b. The numerical value of the autonomous spending multiplier for this economy is

c. If your arithmetic is right, Y decreases when i increases. What is the economic

explanation of this characteristic of the IS relation? 5 points

Question II, continued

b) The LM relation.

a. Calculate the LM relation for this economy. [You must first calculate the money

multiplier and the money supply, M s , then put Y on one side of the LM equation and

everything else on the other side of the equation.] 10 points

b. The numerical value of the money multiplier for this economy is _______

c. If your arithmetic is right, i increases when Y increases. What is the economic

explanation of this characteristic of the LM relation?

Question II, continued

c) General equilibrium Determine the equilibrium values of real GDP, Y, and the interest

rate, i, for the economy of this question.

Top question are already answered

Question II and III answers

IS relation: Y = 600 - 1,000i

LM relation: Y = 100 + 4,000i

General equilibrium: 600 - 1,000i = 100 + 4,000i

i = 10%

Question III new G = 125 from 100

Question III new Ms = 75 from 50

Bottom questions are what I need help on relating to the top questions

a) Explain why P increases when G and Ms increase and the economy expands in the short-run. [Your explanation should reflect Wage Setting and Price Settingbehaviors.]

b) How will the short-run equilibrium values of Y and i differ from those you had hoped for (Y up by 10% from its initial value, assumed equal to the natural rate of output,Yn, while i remained unchanged) when you increased G and Ms as you indicated in Question III, parts b and c? Explain why they will differ as you say.

Question IV, continued

c) In the medium-run, Y will return to its initial equilibrium value, assumed equal to the natural rate of output, i.e., Y* = Y0 = Yn. How will the final values of the following variables compare with their values in the initial equilibrium of Question II part c? [Just circle whether the final values will be greater than, >, equal to, =, or less than, < the initial values.]

P*            >      =      <              P0

i*              >      =      <              i0

I*             >      =      <              I0

C*            >      =      <              C0

(Md/P)*    >      =      <              (Md/P)0

d) Something is dreadfully wrong with the new medium-run equilibrium values of this economy when G and Ms increase by the amounts you (should) have indicated in parts (b) and (c) of Question III. What is the problem? Show your calculations.

Explanation / Answer

High-powered money or you can say narrow money is the monetary base of the economy. It includes currency with the public and cash reserves with the banks. Money supply refers to that stock of money held with the public. Money supply equals to money multiplier times high-powered money.

M = mm * Hs, where

M = money supply

mm = money multiplier

Hs = high-powered money OR monetary base

Money multiplier is known as the greatest extent to which the money supply gets affected as a result of change in monetary base.

Money Multiplier (mm) = 1 / Required Reserve ratio

Here, required reserve ratio = =1/4

Thus,

mm = 1 / (1/4) = 4

Now, given : Hs = 50

Thus, M = mm * Hs = 4 * 50 = 200

a) The IS relation:

Aggregate expenditure (AE) = C + I + G + NX, NX = ( Export - Import)

where,

C = Consumption

I = Investment

G = Government expenditure

NX = Net export

Aggregate expenditure is equal to total output in the economy

Given:

C = 100 + .5 YD = 100 + .5(Y-T)

I = 100 + .1 Y – 500 i

G = 100

T = .2 Y

AE = C + I + G + NX = 100 + .5(Y-T) + 100 + .1 Y – 500 i + 100 = 100 + .5(Y - .2Y) +100 + .1 Y – 500 i + 100

Y - .5Y = 300 - 500i

Y = 600 - 1000i

This equation gives IS curve in the economy. Since, IS curve shows Investment-Saving curve model.

b) The LM relation:

Now, the real money supply is given as:

Ms/P = 200/1 = 200

Md/P = Y – 4000 i (given)

In money market, the equilibrium is the point where money supply is equal to money demand.

Therefore, Ms = Md

200 = Y – 4000 i

Y = 4000i + 200

LM curve makes the combination of income and interest rate in such a way that money demand equals to money supply. Thus,

LM curve is given by the above equation of income and interest rate,

Y = 4000i + 200

The IS-LM (Investment Saving - Liquidity Preference Money Supply) model is a macroeconomic tool where interest rates, real output and money market are interrelated to each other. The intersection of the Investment-Saving (IS) and Liquidity Preference - Money Supply (LM) curves constitute the equilibrium in both markets.

At equilibrium, both IS curve and LM curve intersects.

Therefore, 600 - 1000i = 4000i + 200

5000i = 400

i =400/5000 = 0.08 = 8%

Thus, Y = 4000(0.08) + 200 = 520

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.