1. [Matrix Inversion in IS-LM Model]

Given the IS equation

0.4Y +150r 308.25 = 0,

and the LM equation

0.1Y 250r 61.25 = 0,

find the equilibrium level of national income Y and the interest rate r by using the technique of matrix inversion.

2. [Own Price Elasticity of Demand]

Given a demand function Q = f(P), the own price elasticity of demand is defined as

= ( dQ /dP ) ( P /Q ) .

What is the own price elasticity of demand

(a) for the linear demand function Q = 2003.5P when P = 10.

(b) for the linear inverse demand function P = 1003.5Q when Q = 10.

(c) for the inverse demand function P = Q 3.5 , when (i) Q = 5; (ii) Q = 10.

3. [Profit maximization]

If the producer's cost function is

TC(q) = 200q+0.5q^2 ,

and the demand function is p = 12001.5q

where p is the selling price per unit.

(a) What output q maximizes its profit?

(b) What is the profit-maximizing price, p ?

(c) What is its maximal profit ?