True Cost-of-Living Adjustments:

We may now ask how large the necessary compensation is that leaves our consumers as well off in the second period as in the first? In the example above we used the following utility function: U(C, F) = C^0.5F^0.5. The initial utility was U¹ = 50. Let’s denote the unknown income Y ∗, the demand functions for F and C are:

F₂(p_F , Y^∗) = (0.5 x Y^∗)/P_F , and C₂(p_C, Y^∗) = (0.5 x Y^∗)/P_C,

and the utility is:

U(F₂,C₂) = [(0.5 x Y^∗)/PF]^0.5 [(0.5 x Y^∗)/PC]^0.5 = U¹
= (0.5/P_F)^0.5 (0.5/PC)^0.5  Y^∗ = U¹

Hence, we can solve for Y^∗ as:

Y^∗ = U¹ [ (P₂F/0.5)^0.5 (P₂C/0.5)^0.5]

Now we put in the numbers for the prices and the initial utility level:

Y^∗ = 50 (1.03/0.5)^0.5 (1/0.5)^0.5 = 101.49.

The difference is not big, but the minimum income increase necessary to exactly compensate the consumers is less than the increase in the CPI. The “true” cost-of-living index in this case is Y^∗/Y₁ which is less than the CPI.
The CPI calculates the increase in prices as: Y₂/Y₁, which we can write as:

Y₂/Y₁ = (Y^∗/Y₁) . (Y₂/Y^∗)

The first term on the right-hand side shows the increase in the true cost-of-living and the second term, Y₂/Y^∗, reflects the substitution bias in the CPI. This terms if greater than one because Y₂ > Y^∗, hence the bias is positive. There is no substitution bias if all prices increase at the same rate so that relative prices remain constant. The faster some prices rise relative to others the more pronounced is the upward bias due to the substitution effects.

Latest technology based Economics Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Intermediate Microeconomics homework help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Intermediate Microeconomics, project ideas and tutorials. We provide email based Intermediate Microeconomics homework help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Intermediate Microeconomics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Economics homework help and assignment help services. They use their experience, as they have solved thousands of the Computer assignments, which may help you to solve your complex issues of Intermediate Microeconomics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.