An economy is characterized by the following behavioral equations: C = 100 + .5

Question

An economy is characterized by the following behavioral equations:

C = 100 + .5 Y D

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, H s , is 50, the demand for real balances is

M d /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?

Question II, continued

To repeat, the economy of this question is characterized by the following behavioral equations:

C = 100 + .5 Y D

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, H s , is 50, the demand for real balances is

M d /P = Y – 4000 i

and the price level, P, is initially 1.

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.]

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

To repeat, the economy of this question is characterized by the following behavioral equations:

C = 100 + .5 Y D

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, H s , is 50, the demand for real balances is

M d /P = Y – 4000 i

and the price level, P, is initially 1.

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

rate, i, for the economy of this question. 10 points

Be sure to calculate the correct values of Y and i at general equilibrium, i = 0.1 and Y = 500.

Question III, a continuation of Question II

The economy of Question II is characterized by the following behavioral equations:

C = 100 + .5 Y D

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, H s , is 50, the demand for real

balances is

M d /P = Y – 4000 i

and the price level, P, is initially 1.

In Question II, you calculated the IS and LM relations for this economy and determined the

equilibrium values of Y and i.

a) Sketch the IS and LM curves corresponding to this initial situation. Label your axes and

show numerical values on your axes. That is, sketch the curves to scale so they intersect

at equilibrium Y and i. (The output-axis intercepts of the IS and LM curves are readily

obtained by setting the interest rate to zero). Label the point of general equilibrium where

IS and LM intersect “0.”

Question III, a continuation of Question II

The economy of Question II is characterized by the following behavioral equations:

C = 100 + .5 Y D

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, H s , is 50, the demand for real

balances is

M d /P = Y – 4000 i

and the price level, P, is initially 1.

Suppose you want to increase equilibrium output, Y, by 10% without forcing the interest rate, i,

to increase.

b) By how much must you increase government spending, G, so that equilibrium output, Y,

increases by 10% from the value you determined in Question II when interest rate, i, and

price, P, remain unchanged? Show your calculation.

c) By how much most you increase high powered money, H, and money supply, M s , to keep

interest rate, i, at the value you determined in Question II when output, Y, increases by

10% and price, P, remains unchanged? Show your calculation.

d) On the axes on the previous page (Question III, part a), sketch the shifts in IS and LM

curves when government spending, G, increases as you indicate in part (b) above and

high powered money, H, increases as you indicate in part (c) above. Label the new point

of general equilibrium “1.”

Question IV, a continuation of Questions II and III

Contrary to the assumption—or the hope—that price, P, remains unchanged when government

spending, G, and money supply, M s , increase as you indicated above (Question III parts b and c),

P in fact increases.

a) Explain why P increases when G and M s increase and the economy expands in the short-

run. [Your explanation should reflect Wage Setting and Price Setting behaviors.]

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, Y n , while

i remained unchanged) when you increased G and M s 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 * = Y 0 = Y n . 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 * > = < P 0

i * > = < i 0

I * > = < I 0

C * > = < C 0

(M d /P) * > = < (M d /P) 0

EXTRA CREDIT

Something is dreadfully wrong with the new medium-run equilibrium values of this economy

when G and M s 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

C = 100 + 0.5YD [where YD = Y - T = Y - 0.2Y = 0.8Y]

I = 100 + 0.1Y – 500i

G = 100

T = 0.2 Y

(a) IS equation

Y = C + I + G

Y = 100 + 0.5 x 0.8Y + 100 + 0.1Y – 500i + 100

Y = 300 + 0.4Y + 0.1Y - 500i

Y = 300 + 0.5Y - 500i

(1 - 0.5)Y = 300 - 500i

0.5Y = 300 - 500i

Y = 600 - 1,000i [Equation of IS]

(b) MPC = 0.5

Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.5) = 1 / 0.5 = 2

(c) When Y increases, i (nominal interest rate) increases. This is because, higher income results in higher investment demand, which raises nominal interest rate ceteris paribus.

QUESTION - II (Continued)

(a) Money multiplier (MM) = (1 + Currency deposit ratio, C) / (Currency deposit ratio + Reserve deposit ratio, R)

C = (Currency / Money) / (Deposit / Money) = (1/3) / (2 / 3) = 1 / 2 = 0.5

R = 1 / 4 = 0.25

M = (1 + 0.5) / (0.5 + 0.25) = 1.5 / 0.75 = 2

So, money supply (MS) = High-powered money x MM = 50 x 2 = 100

In money market equilibrium, MS = MD/P

100 = Y - 4,000i

Y = 100 + 4,000i [LM equation]

(b) Money multiplier = 2

NOTE: First 5 sub-questions are answered.

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