Question

1. Consider an economy described by the following: C = 400 +0SY -IA - TRỊ I = 150 -0.18-10 G = 200, T = 2Y, TR = 100 transfers, G- Where consumption, I investment, t is the marginal tax rate, TR government purchases, and is the interest rate. a. Derive the Is relation. (Hint: You want an equation with Y on the left hand side and everything else on the right.) b. What is equilibrium Y if the interest rate is 2% 5% 10% 15% 2. a. Use the following information about money demand and money supply: AM/PY' = 2Y-80i; (M/P* = 4,000 to derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with the interest rate on the left side and everything else on the right.) h. Using the IS equation from Q1 and the LM relation from part a., solve for equilibrium real output Y. (Hint: Substitute the expression for the interest rate given by the LM equation into the is equation and solve for Y.) c. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part b. into either the IS or LM equations and salve for i, If your algebra is correct you should get the same answer from both equations.) d. Solve for the equilibrium values of Cand Iand verify the value you obtained for Y by adding Cl and G. e. Draw a graph of this IS-LM model, labeling everything carefully, including the equilibrium point you found in b.

Answer 1

(1)

(a)

In goods market equilibrium, Y = C + I + G

Y = 400 + 0.5 x (Y - 0.2Y + 100) + 150 + 0.1Y - 10i + 200

Y = 750 + 0.5 x (0.8Y + 100) + 0.1Y - 10i

Y = 750 + 0.4Y + 50 + 0.1Y - 10i

(1 - 0.4 - 0.1)Y = 800 - 10i

0.5Y = 800 - 10i

Y = 1600 - 20i.........(IS equation)

(b)

(i) i = 2%

Y = 1600 - 20 x 2 = 1600 - 40 = 1560

(ii) i = 5%

Y = 1600 - 20 x 5 = 1600 - 100 = 1500

(iii) i = 10%

Y = 1600 - 20 x 10 = 1600 - 200 = 1400

(iv) Y = 15%

Y = 1600 - 20 x 15 = 1600 - 300 = 1300

NOTE: As HOMEWORKLIB Answering Policy, 1st question has been answered.