Question

f. If P increases and M is constant, does the LM curve shit upward and to the left or downward and to the right? 2. IS-LM Model (20 points) Assume that an economy is characterized by the following equations T 600; G 500, 1-800-(50/3)r, M 1200, P M0.SY-50 (1) write the IS curve for the economy, expressing Y as a function of r· (3 points) (2). Write the LM curve for the economy, expressing r as a function of Y. ( points) (3). Solve for the equilibrium values of Y and r, Find public, private and national savings. Does national saving equal investment in the equilibrium? Verify. (6 points) (4) If G increases by 100, what is the new value of Y? How big is the crowding out? (2 points) (5) For parts (1)-(3), how do Y and r change when P - 2.0 (2 points) (6) Write the numerical aggregate demand curve for this economy, expressing P as a function of Y. Graph the AD curve. (4 points) 2. (10 points) If the government announces a rise in taxes, how will the central bank react to this rise, according to the IS-LM model? CHint: there are three possibilities.) 3. (8 points) Suppose that money demand depends on disposable income, so that the equation for the money market becomes MIP LG,Y-T). Analyze the impact of a tax cut in a small open economy on the exchange rate and income under both floating and fixed exchange rates.

Answer 1

(Question 2)

(1) In goods market equilibrium, Y = C + I + G

Y = 100 + (2/3) x (Y - 600) + 800 - (50r/3) + 500

Y = 1400 + [(2Y - 1200)/3] - (50r/3)

3Y = 4200 + 2Y - 1200 - 50r [Multiplying both sides by 3]

Y = 3000 - 50r..........(Equation of IS curve)

(2) In money market equilibrium, (Md/P) = (Ms/P)

0.5Y - 50r = 1200/1 = 1200

50r = 0.5Y - 1200

r = 0.01Y - 24...........(Equation of LM curve)

(3) From money market equilibrium,

0.5Y = 1200 + 50r

Y = 2400 + 100r

In general equilibrium, Y_IS = Y_LM.

3000 - 50r = 2400 + 100r

150r = 600

r = 4

Y = 2400 + (100 x 4) = 2400 + 400 = 2800

C = 100 + (2/3) x (2800 - 600) = 100 + (2/3) x 2200 = 100 + 1466.67 = 1566.67

Private saving (Sp) = Y - C = 2800 - 1566.67 = 1233.33

Public saving (Sg) = T - G = 600 - 500 = 100

National saving (S) = Sp + Sg = 1233.33 + 100 = 1333.33

I = 800 - [(50 x 4)/3] = 800 - 66.67 = 733.33

Since S > I, national saving is not equal to investment.

(4) Since MPC = 2/3 (From consumption function),

Spending multiplier = 1 / (1 - MPC) = 1 / [1 - (2/3)] = 1 / (1/3) = 3

In absence of crowding out, when G increases by 100, Y should increase by (100 x 3) = 300.

New value of G = 500 + 100 = 600. Plugging this in IS condition,

Y = 100 + (2/3) x (Y - 600) + 800 - (50r/3) + 600

Y = 1500 + [(2Y - 1200)/3] - (50r/3)

3Y = 4500 + 2Y - 1200 - 50r [Multiplying both sides by 3]

Y = 3300 - 50r..........(Equation of new IS curve)

Equating with Y_LM,

3300 - 50r = 2400 + 100r

150r = 900

r = 6

Y = 2400 + (100 x 6) = 2400 + 600 = 3000

Increase in Y = 3000 - 2800 = 200

Crowding out effect = 300 - 200 = 100

NOTE: As per Answering Policy, 1st 4 parts are answered.