Question

In: Economics

The demand for money in a country is given by Md= 10,000 - 10,000r +P.Y where...

The demand for money in a country is given by Md= 10,000 - 10,000r +P.Y where Mdis money demand in dollars, r is the interest rate (a 10 percent interest rate means r = 0.1), and is national income. Assume that P.Y is initially 5,000.a)Graph the amount of money demanded (on the horizontal axis) against the interest rate (on the vertical axis).b)Suppose the money supply (Ms) is set by the central bank at $10,000. On the same graph you drew for part a., add the money supply curve. What is the equilibrium rate of interest? Explain how you arrived at your answer.c)Suppose income rises from Y= 5,000 to Y= 7,500. What happens to the money demand curve you drew in part a.? Draw the new curve if there is one. What happens to the equilibrium interest rate if the central bank does not change the supply of money? d)If the central bank wants to keep the equilibrium interest rate at the same value as it was in part b., by how much should it increase or decrease the supply of money given the new level of national income?e)Suppose the shift in part c. has occurred and the money supply remains at $10,000 but there is no observed change in the interest rate. What might have happened that could explain this?

Solutions

Expert Solution

Subpart a

money demand and interest rate are inversely related, as the interesr rate rises the demand for money falls. At r=0.1 Md= 1400units.

Subpart b

The money supply Ms is fixed by the Government, (irrespective of the interest rate), when the government fixes the money supply at $10000, it is a straight line parallel to the vertical axis.

Money demand is a function of income and interest rate. Where Md is directly proportional to PY( as PY increases Md also rises and vuce versa) and inversely propotional to interest rate ( as interest rate rises money demand falls).

Money supply Ms is exogenously fixed by the government.

At equilibrium

Md = Ms

when the Government fixes the Money supply at $10,000 the interest rate is:-

10000-10000r + 5000 = 10000

=> -10000r = -5000

=> r = 1/2 = 0.5

Therefore, the equilibrium interest is at 0.5 when the money supply is fixed at $10,000.

Subpart c

Subpart d

If the Government wants to keep the interest rate at r=0.5 then at y= $7500 and r = 0.5 the money supply is:-

Md = Ms

10000 -10000(0.5) + 7500= Ms

=> Ms = $12500
Therefore, the government should increase its money supply by (12500-10000) $2500.


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