Posted: February 16th, 2017

# calculate the amount of the substitution bias ­ that is, how much extra income does the individual get as a result of the CPI adjustment beyond what is needed to afford the bundle

In class, we talked about the CPI income adjustment and we found out that such adjustment leads to what is called a “substitution bias.” This effectively makes the consumer better off. Consider a numerical example. Suppose the preferences of the representative consumer are captured by the utility function: u(x1,x2) = x1^(1/2)*x2^(1/2). Originally, prices were p1 = p2 = 1 and income was 10. In the next year the price of good 1 doubled. The price of good 2 stayed the same. Calculate the CPI income adjustment. Calculate the new optimal bundle (in class we labeled it C). And lastly, calculate the amount of the substitution bias ­ that is, how much extra income does the individual get as a result of the CPI adjustment beyond what is needed to afford the bundle C? Finally, by how much is the consumer better off as a result of the CPI adjustment relative to his utility before the price change? Draw graph if necessary.

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