Question

Suppose the federal reserve decreases interest rates from 4% to 3%, which leads to an increase in short-run output of 1.5%. if there are no other shocks to the economy, and the resulting change in inflation is 0.375%, what is the value of the parameter?

Answer 1

To find the value of the parameter, use the formula MV=PQ and solve for Q. Calculate the new Q value by multiplying the initial Q value by the change in short-run output. Calculate the new P value by multiplying the initial P value by the change in inflation. Finally, calculate the new MV value by multiplying the new P value by the new Q value.

Step-by-step explanation:

To find the value of the parameter, we need to use the formula MV=PQ. The initial values are MV=4800 and P=110. We can solve for Q by rearranging the formula: 4800 = 110 × Q. Solving for Q, we get Q = 43.64.

The change in short-run output is 1.5%, so we can calculate the new Q value by multiplying the initial Q value by 1.015: 43.64 × 1.015 = 44.34.

The change in inflation is 0.375%, so we can calculate the new P value by multiplying the initial P value by 1.00375: 110 × 1.00375 = 110.41.

Finally, we can calculate the new MV value by multiplying the new P value by the new Q value: 110.41 × 44.34 = 4894.

So, the value of the parameter is 4894.