There is evidence that the rate at which money changed hands rose during the german hyperinflation. this means that
a. velocity rose. if monetary neutrality holds the rise in velocity increased the ratio m/p.
b. velocity rose. if monetary neutrality holds the rise in velocity decreased the ratio m/p.
c. velocity fell. if monetary neutrality holds the fall in velocity increased the ratio m/p.
d. velocity fell. if monetary neutrality holds the fall in velocity decreased the ratio m/p.

The correct answer is b. velocity rose. If monetary neutrality holds the rise in velocity decreased the ratio M/P.

Explanation:

The quantitative theory of money states that in a given period of time, the money supply multiplied by the velocity of money (that is the rate at which moeny changes hands) is equal to the price level multiplied by the amount of goods and services. Mathematically:

By algebraic manipulation we obtain:

Money neutrality means that a change in the supply of money only has an effect on nominal variables, such as the price level, with no effect on real variables such as the real amount of goods and services.

Therefore if we know that the velocity of money rises then the ratio must decrease for money neutrality to hold, that is for to remain constant.

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.