Answer to Question #56720 in Macroeconomics for Domenic

Question #56720

You are given the following information about the commodity and money markets of a closed economy without government intervention.
The Commodity Market
Consumption Function: C=50+2/5Y
Investment Function: I=790-21r

The Money Market
Precautionary and Transactions demand for money : MDT=1/6Y
Speculative demand for money: MDS=1200-18r

Required
Determine the equilibrium levels of income and interest rate for this economy
using a well labelled diagram, illustrate the equilibrium condition in part (i) above

Expert's answer

C = 50 + 2/5Y, I = 790 – 21r
MDT = 1/6 Y, MDS = 1200 -18r, MS = 1250
(i) In equilibrium Y = C + I and MD = MDT + MDS = MS, so:
50 + 2/5Y = 790 – 21r
1/6 Y + 1200 - 18r = 1250,
2/5Y + 21r = 740
1/6Y - 18r = 50 -> 2/5Y - 43.2r = 120, so if we subtract second equation from the first, we will get:
64.2r = 620
r = 9.66%
Y = (740 - 21*9.66)/0.4 = $1343
So, r = 9.66% and Y = $1343 are the equilibrium levels of income and interest rate for this economy.