Please see the details:

ws curve: 𝑊/𝑃= 𝑃^𝑒/𝑃((40/100) + 𝑧 − 10𝑢)
production function: 𝑌 = 2𝑁
job insurance generosity: 𝑍 = 60/100
labor force: 𝐿 = 500
profit margin: 𝑚 = 1
and whose demand is characterized by the equations:
consumption: 𝐶 = 40 + 0.1(𝑌 − 𝑇)
investments:𝐼 = 14 − 20𝑖
government spending: 𝐺 = 40
taxes: 𝑇 = 40
expected inflation: 𝜋𝑒 = 0
Nominal Currency Stock: 𝑀̅ = 1000
actual cash demand: 𝑀^𝑑/𝑃 = 𝑌 − 120𝑖

2. What is the equation of the aggregate supply curve (AO)?
3. What is the equation of the IS curve?
4. What is the equation of the LM curve?
5. What is the equation of the aggregate demand curve (AD)?
6. What is the medium-term equilibrium?
7. Suppose the central bank increases the stock of money to 𝑀̅ = 2000 no effect on expected inflation. What will be the short-term and medium-term effect of this policy change on price level, GDP and real interest rate? Illustrate graph your answer.
8. Returning to 𝑀̅ = 1000. Suppose the government raises its spending to G = 500. What will be the short-term and medium-term effect of this policy change on
the price level, GDP and the real interest rate?

C = 1275 + 0.5(Y-T) – 200r

I = 900 – 200r

Real Money demand, L = 0.5Y – 200i

Expected inflation, ? = 0

Full employment output, = 4600

a.) Suppose that T = G = 450 and M = 9000

Find an equation describing the IS curve

Find an equation describing the LM curve

Find an equation for the aggregate demand curve (Hint: Use IS and LM equations to find a relationship between Y and P)

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

b) Suppose M = 4500, T and G remain the same.

What is the equation for the aggregate demand curve?

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

c.) Suppose T = G = 330 and M = 9000

What is the equation for the aggregate demand curve?

What are the general equilibrium values of output, consumption, investment, real interest rate, and price level?

2. Assume that households’ consumption function is given by C(Y − T) = 50 + 0.75(Y − T), that firms’ investment function is I(r) = 150 − 10r, government spending is G = 150, and the tax bill T = 200.

(a) What is the Marginal Propensity to Consume (“MPC”)?

(b) What is the equilibrium level of real GDP, in the goods market, if the real interest rate is 5%? (Plug in r = 5 for 5%, rather than 0.05 This is an assumption about the way we scale the coefficients in the investment function.)

(c) Solve for the equation of the IS Curve (“Investment-Savings”). How will this equation change if government spending increases to 200? The money supply is MS = 3000 and the price level is P = 4. Money/liquidity demand is given by Md/P = L(r, Y ) = Y − 50r.

(d) Solve for the equation of the LM Curve (“Liquidity-Money”).

(e) Based on your answers to the previous two questions, what are the equilibrium levels of the real interest rate and real GDP? (G is back to 150.)

(f) Assume now that P is unknown. Solve for the equation of the Aggregate Demand curve (“AD”)

A) Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run aggregate supply curve is horizontal at P = $1.0. The aggregate demand curve is Y = 2(M/P) and M = 1,500.

i) If the economy is initially in long-run equilibrium, what are the values of P and Y?

ii) What is the velocity of money in this economy?

iii) If M increases to 2,000, what are the new short-run values of P and Y?

iv) Once the economy adjusts to long-run equilibrium at M = 2,000, what are P and Y?

B) Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run aggregate supply curve is horizontal at P = $1.0. The aggregate demand curve is Y = 3(M/P) and M = 1,000.

i) Suppose a supply shock moves the short-run aggregate supply curve to P=$1.5. What are the new short-run P and Y? What will be the new long-run P and Y?

ii) Suppose that immediately after the supply shock the Federal Reserve Bank wanted to hold output at its long-run level. What level of M would be required? If this level of M were maintained, what would be long-run equilibrium P and Y?

C) Use the aggregate demand/aggregate supply model to illustrate graphically the impact in the short run and the long run of the following changes. (Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; v. the short-run equilibrium values; and vi. the long-run equilibrium values). Also, state what happens to prices and output in the short run and the long run.

i) The Federal Reserve Bank engages in expansionary monetary policy.

ii) Climate change causes reduced food production.

iii) Labor unions are banned.