Question

The following equations describe an economy (think of C, I, G, etc as being measured in billions and i as a percentage; a 5 percent interest rate implies i = 5)

           

C = 0.8 (1 – t) Y

           t = 0.25

           I = 900 – 50i

           G = 800

           L = 0.25Y – 62.5.i

           M / P = 500

Show that a given change in the money stock has a larger effect on output the less interest sensitive is the demand for money.

Answer 1

we start by focus on the goods market and thus, we start by computing the equation.

C = 0.8 (1 – t) Y +  I = 900 – 50i + G = 800

Y=C+I+G

Y=0.6Y+900-50i+800

0.4Y=1700-5Oi

Y=4250-125i is the goods market equation

money market equation is created through the following process

Money Demand= Money Supply

0.25Y – 62.5.i =M / P = 500

0.25Y- 62.5i = 500

0.25Y= 62.5i+500

Y= 250i+2000 is the money market equation

we equate the two equations

4250-125i=250i+2000

2250=375i

i= 6%

a unit change in income (Y) will lead to 6% increase in the interest rates (i).