1. 1 Cost of Living

2. 2 cost of living On the next several slides we want to explore the economic concept called the cost of living. We typically look at a price index to help us understand the cost of living. In order to do this let’s first think about some examples of consumer optimum points. Say that you have income of $20, the price of x is $3, the price of y is $4. Now if you spent all of your income on x you could buy 6 2/3 x or if you spent all your money on y you could buy 5 y. Note that each time an additional unit of x is purchased, 3/4 of a y must be given up.

3. 3 cost of living y x (0, 5) (6 2/3, 0) From the previous screen I have taken information about the budget line and have drawn in the budget line. Plus I have added the fact that when the consumer faces this budget line they end up purchasing the basket (4, 2). (4, 2) We know that when the consumer ends up at point (4, 2) the are as happy as they can be at this time. In fact they are at a point of tangency between the budget line and their highest possible indifference curve.

4. 4 cost of living y x (0, 5) (6 2/3, 0) In this diagram you can see the optimum point for the consumer. (4, 2)

5. 5 cost of living y x (0, 5) (6 2/3, 0) Now let’s say that there are some changes in the world. The price of x becomes 4(it used to be 3), and the price of y becomes 2(used to be 4). Now the new budget line would have: 1) if all income(no change in this example) is spent on y, 10 y could be bought. 2) 5 x could be bought if all is spent on x. (4, 2) In this example the original optimum point could also be purchased at the new prices: (4)(4) + (2)(2) = 20.

6. 6 cost of living new old x y In this diagram I put just the new and the old budget lines. Note that the same original basket can be purchased under either set of prices. With the new budget we know the consumer will not end up to the right of the original basket because any of those baskets on the new budget could have been purchased by the consumer under the old set of prices, but the consumer didn’t buy them. Therefore, they could not have been preferred to the basket.

7. 7 cost of living new old x y When I put in the indifference curve tangent to the old budget line you can see the individual will not end up at the original basketunder the new budget because it isn’t tangent there now. You know the consumer will not end up on the new budget line way up in the upper left - also left of the indifference curve. Those points are less preferred because they have to be on a lower indifference curve.

8. 8 cost of living y x (0, 5) (6 2/3, 0) We conclude that in this example the consumer will actually end up on a higher indifference curve at the later prices compared to the earlier prices. Thus, the consumer is happier under the new prices than under the old prices. (4, 2) Note this is a special example because the consumer can buy the same basket under either set of prices.

9. 9 cost of living Now in this example we had original basket x = 4 and y = 2. Under the original prices of Px = 3, Py = 4 the cost of living at the original basket was (3)(4) + (4)(2) = 20. The consumer price index looks at the cost or ‘price’ of a basket of goods over time. If we look at the original basket and original prices in this example we see the cost of living is 20. Now the new prices are Px = 4, Py = 2. The cost of the original market basket is still 20 = (4)(4) + (2)(2).

10. 10 cost of living In this example the consumer price index would show no change in consumer prices. What is interesting about this example is that although one price went up and one went down, the original basket cost stayed the same- no CPI change - BUT the level of happiness for the consumer went up. In this sense you could say that the CPI is a misleading indicator of the cost of living. It measures the cost of a basket of goods - not the cost of a level of happiness. Since the consumer ends up happier in our example (at the same cost), the cost of having the original happiness went down. Thus, the CPI overstates the cost of maintaining a given level of happiness.

11. 11 steak and potatoes potatoes steak Note in this example the order of preference for the baskets of goods (steak, potatoes) (2, 2) is preferred to (2, 1) is preferred to (1, 2) is preferred to (1, 1)

12. 12 steak and potatoes potatoes steak Now say in some year Ps = $2 and Pp = $1 and the consumer has $4 of income. The budget line is drawn in and the optimum for the consumer is 1 steak, 2 potatoes.

13. 13 steak and potatoes potatoes steak In a later year let’s say prices change such that steak is lowered to $1 and potatoes rise to $2. The new budget line is the dashed line. Note at the new prices more steak is bought when steak is at a lower price and less potatoes are bought when potato prices went up.

14. 14 steak and potatoes Also note on the previous screen that after the price change the consumer is better off. Now let’s look at the original basket (as is done with the consumer price index). At the old prices the basket cost $4. Under the new prices the basket costs $5. We can see from the consumer preferences that this old basket is less preferred than the new basket. The consumer price index would indicate a 25% increase in prices and the consumer is still better off. Why?

15. 15 steak and potatoes The CPI follows the cost of fixed basket of goods over time. Consumers do not buy a fixed basket of goods over time. They tend to shift to goods that have prices lowered and away from goods that have had price increases. In this regard the CPI overstates the true impact of inflation. It measures inflation of a fixed basket of goods. What would really be good is to look at the cost of buying a fixed level of happiness. This method can not be devised. So we live with a measure that has problems and recognize what those problems are.