An economy is described by the following? equations: Desired consumption C d = 1

Question

An economy is described by the following? equations:

Desired consumption

Cd = 150? +0.5(Y-T?)-500r

Desired investment

Id =100-500r

Real money demand L =0.5Y-1,000r

Money supply M = 1,500

Full-employment output Y= 500

Government purchases G= 250

Taxes T = 250

Assume that expected inflation is zero so that money demand depends directly on the real interest rate.

a. Calculate the long-run general-equilibrium values of:

Output

(Y):

The real interest rate

(r):

round to three decimalplaces)

The price level

(P):

(round to two decimal places)

Investment

(I):

(round to two decimal places)

Explanation / Answer

The IS curve is found from the equation Y = Cd + Id + G = 150 + 0.5(Y - 250) - 500r + 100 - 500r+ 250,

or 0.5Y = 375 - 1000r,

or Y = 750 - 2000r. -- IS equation

The LM curve comes from the equation M / P = L, which in this case is 1500 / P = 0.5Y - 1000r

1500/P = 0.5Y- 1000r,

or Y= (3000 / P) + 2000r. --- LM equation

A.

1. The long run equlibrium level of output is same as full employment output so long run general equilibrium value of Y = $500.

2. At full employment, Y = 500.
Put this in the IS curve gives,

500 = 750 - 2000r,

2000r = 250

r = 0.125

So the equilibrium real interest rate r = 0.125

3. Plugging the values for Y and r in the LM curve gives

500 = (3000 / P) + (2000 x 0. 125)

250 = 3000 / P,

which has the solution P = 12.

So equilibrium price level is $12.

4. Investment is I = 100 - (500 x 0.125) = $37.5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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