In a certain economy, the components of planned spending are given by:
c = 500 + 0.8(y - t) - 300r
ip = 200 - 400r
g = 200
nx = 10
t = 150
given the information about the economy above, what would be the impact on autonomous expenditures of a one-percentage-point increase in the real interest rate?
a. autonomous expenditures would increase by 35 units.
b. autonomous expenditures would decrease by 70 units.
c. autonomous expenditures would decrease by 35 units.
d. autonomous expenditures would decrease by 7 units

D. Autonomous expenditures would decrease by 7 units

Explanation:

The interest rate affects two components of the autonomous expenditure: consumption and investment. (Look for the equations that has the variable r on it)

In the consumption the impact of one percent increase is calculated as follows:

C = 500 +0.8(Y-T) - 300(r+1%)

C= 500 +0.8(Y-T) - 300r - 300 * 1%

C= 500 +0.8(Y-T) - 300r - 300 * 1%

C= 500 +0.8(Y-T) - 300r - 3 > -3 units is the impact over consumption.

Now, let´s analyze the impact on investment.

Ip = 200 - 400r

Ip = 200 - 400*(r+1%)

Ip = 200 - 400r - 400*1%

Ip = 200 - 400r - 4 > -4 units is the impact over investment

Then, the total effect over autonomous expenditures = -4 + (-3) = -7

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