A country's central bank is engaging in monetary contraction, with M going from M0=40 to M1=20. Its economy is as follows. Goods: slc = 3 MPC = 0.7 G = 10 T = 9 Before the policy, the goods market equilibrium is at Y0 = 54. Financial: I = 18-200r Before the policy, the loans market equilibrium is at r = 4.25% and I = 9.5 Money: M0 = 40 P0 = 2 M/P = 0.02 / (r - Y/5000)^2 and finally, Labor: w = MPL = 0.5 * 4.5 * 16^0.6 / L^0.5 w = EP / P0 * L^0.5 Where workers currently expect the price level of EP=2. There are four endogenous variables that adjust in response to shock/policy: Y, I, r, P. The policy variable of interest is M. Therefore, let's approach our solution by first recognizing that all other letters are just constants and plug them in. For example: Y = 2 + 0.5(Y-6)+7+I becomes Y = 12 + 2*I First, express the goods market as expenditure being a linear function of investment I of the form: Y = a + b*I where a and b are parameters (numbers). 1. How does the monetary contraction directly and immediately affect the goods market? 2. Now compose the IS curve out of your goods market expression and the financial market from the question prompt. Again, express it as a linear function of expenditure Y of interest rate r of the form Y = c + d*r, where c and d are parameters. 3. Now compose the IS curve out of your goods market expression and the financial market from the question prompt. Again, express it as a linear function of expenditure Y of interest rate r of the form Y = c + d*r, where c and d are parameters. and type it up 4. Convert the money market equilibrium condition from the initial prompt to an LM curve of the form: r = f*P^0.5 + g*Y where f, g are parameters. Note: Use the new M1=20 to eliminate M too. Type up the LM 5. Compose the AD equation. To do that, use your LM to sub out r from your IS. You will get: Y = c + d*( f*P^0.5 + g*Y) Express it as Y = h + i*P^0.5 where h and i are parameters. Type it up 6. Combine the labor demand equilibrium condition with a production function Y = 4.5*16^0.5*L^0.5 to express the AS curve in the form (EP/P)^0.5 = j / Y where j is a parameter. Type up 7. Now take your AD function from before -- the one of the form Y = h + i*P^0.5 and express your AS as P^0.5 = EP^0.5 * Y / j plug in EP=2. Then plug in AS for P^0.5 in AD. You will get Y = h + i * (1.41 * Y / j) and solve for the short-term equilibrium Y.
A country's central bank is engaging in monetary contraction, with M going from M0=40 to M1=20. Its economy is as follows.
Goods:
slc = 3
MPC = 0.7
G = 10
T = 9
Before the policy, the goods
Financial:
I = 18-200r
Before the policy, the loans market equilibrium is at r = 4.25% and I = 9.5
Money:
M0 = 40
P0 = 2
M/P = 0.02 / (r - Y/5000)^2
and finally, Labor:
w = MPL = 0.5 * 4.5 * 16^0.6 / L^0.5
w = EP / P0 * L^0.5
Where workers currently expect the price level of EP=2.
There are four endogenous variables that adjust in response to shock/policy: Y, I, r, P. The policy variable of interest is M. Therefore, let's approach our solution by first recognizing that all other letters are just constants and plug them in.
For example: Y = 2 + 0.5(Y-6)+7+I becomes Y = 12 + 2*I
First, express the goods market as expenditure being a linear function of investment I of the form:
Y = a + b*I
where a and b are parameters (numbers).
1. How does the monetary contraction directly and immediately affect the goods market?
2. Now compose the IS curve out of your goods market expression and the financial market from the question prompt.
Again, express it as a linear function of expenditure Y of interest rate r of the form
Y = c + d*r,
where c and d are parameters.
3. Now compose the IS curve out of your goods market expression and the financial market from the question prompt.
Again, express it as a linear function of expenditure Y of interest rate r of the form
Y = c + d*r,
where c and d are parameters.
and type it up
4. Convert the
r = f*P^0.5 + g*Y
where f, g are parameters.
Note: Use the new M1=20 to eliminate M too.
Type up the LM
5. Compose the AD equation. To do that, use your LM to sub out r from your IS. You will get:
Y = c + d*( f*P^0.5 + g*Y)
Express it as
Y = h + i*P^0.5
where h and i are parameters.
Type it up
6. Combine the labor demand equilibrium condition with a production function Y = 4.5*16^0.5*L^0.5 to express the
(EP/P)^0.5 = j / Y
where j is a parameter.
Type up
7. Now take your AD function from before -- the one of the form
Y = h + i*P^0.5
and express your AS as
P^0.5 = EP^0.5 * Y / j
plug in EP=2.
Then plug in AS for P^0.5 in AD. You will get
Y = h + i * (1.41 * Y / j)
and solve for the short-term equilibrium Y.
Type up
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