Suppose that money demand is given by M SY030 where Yis 100

Suppose that money demand is given by M SY(0.30-) where $Yis $100 and i denotes the interest rate in decimal form. Also, suppose that the supply of money is $20. Calculate the equilibrium interest rate as a percent. The equilibrium interest rate is %. (Round your response to two decimal places.)

Solution

Part (a)

If Y = $100 then Md = 100*(0.30 – i) = 30 – 100*i.

Ms = $20

To solve money market equilibrium level of interest rate, it must be the case that: Md = Ms

Then 30 – 100*i = 20
100*i = 10
i = 10.00%

Part (b)

If Y = $70 then Md = 70*(0.22 – 1.2*i) = 15.4 – 84*i

To meet the interest rate target of 10%, then central bank must set Ms = Md = 15.4 – 84*0.1 = 15.4 – 8.4 = $7.00