Answer to Question #215920 in Macroeconomics for Collins

Question

Suppose that the following system of equations describe the macroeconomy of a
hypothetical country:
Y= C(y)+I(i)+G : IS or goods market
M/p=L(i,y) : LM or money market

a) Get the total differentials of the above system of equations and put your answer
in matrix representation.
b) Taking money supply and government expenditure as exogenous and the price
level as fixed, determine and provide economic intuition for the signs and
magnitudes of the following multipliers
i)
dY/dG
ii)
di/dG
c) For a simultaneous increase in both the interest elasticity of investment and
interest elasticity demand for money parameters, determine the net effect on the
values of the multipliers in part b).
d) For a horizontal LM curve, determine the numerical values of your answers in
part b) above if:
Marginal propensity to consume=5/6

Tax rate=0.25
Interest elasticity of investment=5
Interest elasticity of demand for money=50
Income elasticity of demand for money=2

Answer 1

$Y=3,000+0.5(Y-0.2Y)+2,000+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,000-5,500+0.2Y\\ Y=8,500+0.2Y\\ 0.8Y=8,500\\ Y=10,625$

$Y=3,000+0.5(Y-0.2Y)+1900+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+1900+2,500+6,500-5,500-0.2Y\\ Y=13900-5,500+0.2Y\\ Y=8,400+0.2Y\\ 0.8Y=8,400\\ Y=10,500$

$Y=3,000+0.5(Y-0.2Y)+2,000+2,800+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,300-5,500+0.2Y\\ Y=8,800+0.2Y\\ 0.8Y=8,800\\ Y=11000$