# velocity change

1. Money demand in an economy in which no interest is paid on money is

M^d / P = 500 + 0.2Y - 1000i.

a) Suppose that P = 100, Y = 1000, and i = 0.10. Find real money demand, nominal money demand, and velocity.

b) The price level doubles from P = 100 to P = 200. Find real money demand, nominal money demand, and velocity.

c) Starting from the values of the variables given in part (a) and assuming that the money demand function as written holds, determine how velocity is affected by an increase in real income, by an increase in the nominal interest rate, and by an increase in the price level.

2. Mr. Midas has wealth of $100,000 that he invests entirely in money (a checking account) and government bonds. Mr. Midas instructs his broker to invest $50,000 in bonds, plus $5000 more in bonds for every percentage point that the interest arte on bonds exceeds the interest arte on his checking account.

a) Write an algebraic formula that vies Mr. Midas's demand for money as a function of bond and checking account interest rates.

b) Write an algebraic formula that gives Mr. Midas's demand for bonds. What is the sum of his demand for money and his demand for bonds?

c) Suppose that all holders of wealth in the economy are identical to Mr. Midas. Fixed asset supplies per person are $80,000 of bonds and $20,000 of checking accounts. Checking accounts pay no interest. What is the interest rate on bonds in asset market equilibrium?

3. Assume that the quantity theory of money holds and that velocity is constant at 5. Output is fixed at its full-employment value of 10,000 and the price level is 2.

a) Determine the real demand for money and the nominal demand for money.

b) In this same economy the government fixes the nominal money supply at 5000. With output fixed at its full-employment level and with the assumption that prices are flexible, what will be the new price level? What happens to the price level if the nominal money supply rises to 6000?

4. Consider an economy with a constant nominal money supply, a constant level of real output Y = 100, and a constant real interest rate r = 0.10. Suppose that the income elasticity of money demand is 0.5 and the interest elasticity of money demand is -0.1.

a) By what percentage does the equilibrium price level differ from its initial value if output increases to Y = 106 (and r remains at 0.10)?

b) By what percentage does the equilibrium price level differ from its initial value if the real interest increase to r = 0.11 (and Y remains at 100).

c) Suppose that the real interest rate increase to r = 0.11. What would real output have to be for the equilibrium price level to remain at its initial value?

5. Suppose that the real money demand function is

L (Y, r + π^e) = (0.01Y) / (r + π^e')

where Y is real output, r is the real interest rate, and π^e is the expected rate of inflation. Real output is constant over time at Y = 150. The real interest rate is fixed in the goods market at r = 0.5 per year.

a) Suppose that the nominal money supply is growing at the rate of 10% per year and that this growth rate is expected to persist forever. Currently, the nominal money supply is M = 300. What are the values of the real money supply and the current real price level? (Hint: What is the value of the expected inflation rate that enters the money demand function?)

b) Suppose that the nominal money supply is M = 300. The central bank announces that form now on the nominal money supply will grow at the rate of 5% per year. If everyone believes this announcement, and if all markets are in equilibrium, what are the values of the real money supply and the current price level? Explain the effects on the real money supply and the current price level of a slowdown in the rate of money growth.

6. The income elasticity of money demand is 2/3 and the interest elasticity of money demand is -0.1. Real income is expected to grow by 4.5% over the next year, and the real interest rate is expected to remain constant over the next year. The rate of inflation has been zero for several years.

a) If the central bank wants zero inflation over the next year, what growth rate of the nominal money supply should it choose?

b) By how much will velocity change over the next year if the central bank follows the policy that achieves zero inflation?

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#### Solution Summary

The quantity theory of money is referenced.

Calculus with a lot of examples

Let f be defined as follows.

f(x)=x^2-3x

(a) Find the average rate of change of y with respect to x in the following intervals.

from x = 6 to x = 7

from x = 6 to x = 6.5

from x = 6 to x = 6.1

(b) Find the (instantaneous) rate of change of y at x = 6.

The demand for Sportsman 5 X 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.)

p = f(x) = ?0.1x^2 ? x + 40

(a) Find the average rate of change in the unit price of a tent if the quantity demanded is between the following intervals.

between 4400 and 4450 tents $ per 1000 tents

between 4400 and 4410 tents $ per 1000 tents

(b) What is the rate of change of the unit price if the quantity demanded is 4400?

$ per 1000 tents

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the following function.

P=f(t)=3t^2+2t+1

Find the rate of population growth at t = 11 min.

bacteria per minute

The position function of an object moving along a straight line is given by

s = f(t).

The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a.

A ball is thrown straight up with an initial velocity of 144 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 144t ? 16t^2.

(a) What is the average velocity of the ball over the following time intervals?

[4,5] ft/sec

[4,4.5] ft/sec

[4,4.1] ft/sec

(b) What is the instantaneous velocity at time t = 4?

ft/sec

(c) What is the instantaneous velocity at time t = 8?

ft/sec

Is the ball rising or falling at this time?

rising falling

(d) When will the ball hit the ground?

t = sec