Assume that the consumption function is given by C = 200 + 0.7(Y - T) , the tax function is given by T = 100 + t Y, and 1
Y = 50K^0.5L^0.5, where K = 100 and L = 100. If t increases from 0.2 to 0.25, then consumption decreases by:
1

Question

Quizplus · Accepted Answer

Substituting the given values in the tax function, we have:
T = 100 + tY
T = 100 + 0.25(50K + 5S + 0L)
T = 100 + 12.5K + 1.25S + 0
T = 212.5
Substituting the value of Y and T in the consumption function, we have:
C = 200 + 0.7(Y - T)
C = 200 + 0.7(50K + 5S + 0L - 212.5)
C = 200 + 35K + 3.5S - 148.75
C = 35K + 3.5S + 51.25
Now, if t increases from 0.2 to 0.25, the value of T will increase from 187.5 to 212.5. 
Substituting the new value of T in the consumption function, we have:
C = 35K + 3.5S + 51.25 + 0.7(50K + 5S + 0L - 212.5) 
C = 35K + 3.5S + 51.25 + 0.7(50K + 5S - 212.5) 
C = 35K + 3.5S + 51.25 + 0.7(50K + 5S - 212.5) 
C = 35K + 3.5S + 51.25 + 24.5K + 2.45S - 148.75
C = 59.5K + 5.95S - 97.5
The decrease in consumption is:
New Consumption - Old Consumption
(59.5K + 5.95S - 97.5) - (35K + 3.5S + 51.25)
24.5K + 2.45S - 148.75
= 24.5(100) + 2.45(100) - 148.75
= 2450 - 148.75
= 2301.25
Therefore, consumption decreases by $2,301.25, which is closest to option C: 175.

Assume That the Consumption Function Is Given by C =