Question

If you earned $10-an-hour in 2005 when the CPI was 100, and you earn $11-an-hour today when the CPI is 120, then your real wage rate has _____ since 2005

A) increased by 20%
B) remained the same
C) decreased
D) increased by 10%

please do it step by step

Answer 1

For Year 2005

CPI_{​​​​t} = 100

C_{​​​​​​t} = 10

After Substituting Values in Formula,

100 = (10/C_{​​​​​​0} )* 100

C_{​​​​​​0 =} (10/100 )* 100

C​​​​​​_{​​​​​​0}= 10

Here, C_{​​​​​​0}= C_{​​​​t}, Means 2005 was base Year.

Now,

CPI_{​​​​t} = 120

And C_{​​​​​​0} = 10 (Calculated in previous part)

After Substituting Values in Formula

120 = (C_{​​​​​​t} /10 )*100

C​​​​​_{​​​​​​t} =  (120/100 )*10

C_{​​​​​t}= 12

But, according to question C_{​​​​​​t} is 11.

So, Answer is C(Decreased), Because Real wage is decreased. It should be 12 but it is 11.