Question II An economy is characterized by the following behavioral equations: C

Question

Question II

An economy is characterized by the following behavioral equations:

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.

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.]

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

______

If your arithmetic is right, Y decreases when i increases. What is the economic explanation of this characteristic of the IS relation?

b)The LM relation.

Calculate the LM relation for this economy. [You must first calculate the money multiplier and the money supply, Ms, then put Y on one side of the LM equation and everything else on the other side of the equation.]

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

If your arithmetic is right, i increases when Y increases. What is the economic explanation of this characteristic of the LM relation?

c)General equilibrium Determine the equilibrium values of real GDP, Y, and the interest rate, i, for the economy of this question.

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

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 andLM curves are readily obtained by setting the interest rate to zero). Label the point of general equilibrium where IS and LM intersect “0.”

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.

By how much most you increase high powered money, H, and money supply, Ms, 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.

On the axes on the previous page (Question III, part a), sketch the shifts in IS andLM 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.”

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.]

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

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

(A)

(1) IS relation

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

I = 100 + 0.1Y – 500i

G = 100

T = 0.2 Y

In goods market equilibrium,

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]

(2) MPC = 0.5

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

(3) When i increases, it results in higher investment demand, which raises aggregate demand (real GDP).

(B) LM relation

(1)

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]

(2) Money multiplier = 2

(3) When Y increases, consumption and investment demand rises accordingly and so, interest rate rises ceteris paribus.

(C) General equilibrium

In general equilibrium, IS = LM

600 - 1,000i = 100 + 4,000i

5,000i = 500

i = 500 / 5,000 = 0.10 (10%)

Y = 100 + (4,000 x 0.1) = 100 + 400 = 500

Note: First 7 sub-questions are answered.

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