Question

Assume that the consumption function is given by C = 200 + 0.75(Y ? T). Government purchases and taxes are both 100. Planned investment is derived as follows: there are many ideas, whose cost of implementation are all 3. Ideas are indexed by j > 0. Idea j produces j units of return next year. Index j follows an exponential distribution on (0, ?) with density 100e ?j , j > 0. Derive the IS curve.

Answer 1

Answer:-

(1) In goods market equilibrium, Y = C + I + G
Y = 200 + 0.75(Y - 100) + 200 - 2,500r + 100
Y = 500 + 0.75Y - 75 - 2,500r
0.25Y = 425 - 2,500r
Y = 1,700 - 10,000r [IS Equation]
(2) In money market equilibrium, (Md / P) = Y - 10,000r
(1,000 / P) = Y - 10,000r
Y = (1,000 / P) + 10,000r [LM equation]
(3) From IS equation,
10,000r = 1,700 - Y
Substituting in LM equation,
Y = (1,000 / P) + 1,700 - Y
2Y = (1,000 / P) + 1,700
Y = (500 / P) + 850 [AD Curve]