Question

Suppose the following equations describe the relationship between the long-run shares of spending in GDP and the interest rate (R), measured in decimal fractions (that is, R = 0.05 means that the interest rate is 5 percent).

Equations: C/Y* = 0.7 – 0.2(R - .05) and I/Y* = 0.2 – 0.8(R - .05)
X/Y* = .0 – 0.95(R - .05) and G/Y* = .2
Use algebra to determine the long-run shares of spending in GDP for a long-run government share of 17 percent rather than 20 percent (that is, G/Y* = 0.17).
C percentage = %
I percentage = %
X percentage = %
G percentage = %

Answer 1

The student asks for the calculation of long-run shares of GDP given a change in government spending from 20% to 17%. Adjustments to the other components will be necessary to maintain the total shares adding up to 1.

Step-by-step explanation:

The student is asking for the determination of long-run shares of spending in GDP when the government share changes from 20 percent to 17 percent.

To find the new long-run shares of the components of GDP (C, I, X, G), we must first change the G/Y* equation to reflect the new government spending share, which is now 0.17 instead of 0.2. The equations provided are:

• C/Y* = 0.7 – 0.2(R - .05)
• I/Y* = 0.2 – 0.8(R - .05)
• X/Y* = 0.0 – 0.95(R - .05)
• G/Y* = 0.2 (this will change to G/Y* = 0.17)

To maintain the balance that the total shares must add up to 1 (or 100%), a decrease in G/Y* implies the other components must adjust accordingly.