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Income and substitution effects

January 20, 2012

Optimal choice when faced with a budget constraint involves moving to an indifference curve that is tangential to the budget line.

But if the prices a good changes, it will change the budget line. Here we will take the opportunity to use the “two good” model to specifically focus on the effects of the price change of one good, by considering good X on the horizontal axis and “AOG” or “all other goods” on the vertical axis. This allows us to see how much someone can spend on all other goods, once they have finished spending on good X.

If the price of good X rises, then the budget line will pivot inwards around the point where it crosses the vertical axis. At the vertical intercept, the consumer is spending all his money on “all other goods” and not buying any of good X, so a price change in good X won’t change anything. But the horizontal intercept will be different, as the consumer is then spending all his money on good X, which is now more expensive, so obviously he can afford less given his budget.

Here at the original budget constraint of B1, the optimal bundle is at A, where the consumer has aX of good X and aAOG of all other goods. When the price of X increases, the budget line shifts to B2. Here the optimal bundle is at B, where the consumer is consuming less of good X and more of other goods.

Two things have gone on here. There is a substitution effect whereby the consumer is deciding to substitute some of good X for some other goods because X is now more expensive relative to other goods. There is also an income effect whereby the fact that X has got more expensive whilst other goods are unchanged in price, means that the consumer is now relatively poorer than he was before, his money doesn’t go as far.

To show how much of the overall change in spending on the different goods is due to the substitution effect, we consider what would happen if we were ‘compensating’ the consumer by giving him enough of a raise in income to allow him to stay at the same level of utility as he was on at bundle A, now that good X has become more expensive.

We can break down the substitution and income effects like this:

Here we have drawn a new budget line (the black dashed line) with the same slope as the final budget line (B2), indicating the same relative prices between X and other goods as the final relative prices after the price change. This has been moved to the point that is tangential to the indifference curve that the original bundle, A, was on. Now this budget line effectively represents an increased budget, because it is a parallel shift outwards from B2. It shows us the budget that the consumer would have needed, to stay at the original level of utility, the same indifference curve as he was on at bundle A. However A would not be the optimal choice bundle here, it would be bundle C. Bundle C gives the same level of utility as bundle A, but it would satisfy the new relative prices after the price change. This shows us the substitution effect. If the consumer was compensated by being given enough raise in income to allow him to stay at the same level of utility as he was on at bundle A, he would have responded to the change in relative prices by shifting his spending to buy less good X and more other goods, hence the move from A to C.

The rest of the effect is the income effect. The shift from C to B, where the consumer has less money to spend on good X and also less money to spend on other goods, is as a result of the income effect of the price change making him poorer overall.

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