Thursday, 10/25/01
Problem 1 - Suppose a consumer has income of $20, the price of X is $2 per unit, and the price of Y is $4 per unit.
When you draw a budget line, the easiest thing to do is plot a couple of points and connect the dots. What are the easiest points to plot? Just like when we had to draw Production Possibilities Frontiers, the easiest ones are the two intercepts on the axes. You should always plot those points first.
The budget line is determined by the prices of all the things that can be bought and the income of the agent. Here, there are two goods, so we must care about three things total: income, price of X and price of Y. Anytime any of these three things change, we need to re-evaluate what the budget line looks like. One way to go about doing part b is to draw the original budget line on a new diagram for each case and add the new modified budget line for that case onto that diagram.
Problem 2 - Suppose your willingness to pay for ice cream were as follows:
| Gallons of Ice Cream | Willingness to Pay |
|---|---|
| 1 | $10 |
| 2 | $7 |
| 3 | $5 |
| 4 | $3 |
| 5 | $2 |
| 6 | $1 |
In this table, we are telling you how much happiness you get from the Nth gallon of ice cream. For example, when you eat a third gallon of ice cream, that third gallon is $5 good in your opinion. What's the rule for deciding how much to buy? You buy until the marginal benefit equals the marginal cost; until price = happiness from that last gallon.
For part b, recall what surplus is - happiness you didn't have to pay for. We tell you how happy each gallon makes you. But you only pay $3 for each gallon. So how much bonus did you get for the first gallon? How much bonus did you get on the second gallon? Etc...
Problem 3 - A consumer purchases two goods, X and Y. In period 1, this consumer has income of $30, the price of both goods is $1 and she buys 10 units of X and 20 units of Y. In Period 2, the price of X remains at $1, the price of Y rises to $2, and her income rises to $50.
Part a will look like the sweater example in class. What you want to do is draw the Period 1 budget line on a diagram with X and Y on the axes. Then draw Period 2's budget line over this. Now look at the sweater example from lecture.
The way the CPI works is kind of funky. What the government does is they take a list of items that they think is representative of what an "average" person buys. They then go out to stores and ask how much the store's price for each item on the list is. They do this for thousands of stores across the country and come up with an average price for each item in the list. Through some magic hand waving, they combine all of these prices for all of these items into one number. If the CPI number goes up, this is interpreted as a rise in the cost of living. How so? Because the combined prices of what an "average" person buys will now take more money to actually purchase. This is what people are talking about when you hear stuff like "Cost of Living Adjustment" or some city being expensive to live in. It has something to do with the CPI in that city.
If you look at Period 1 and Period 2, what has happened to prices? We imagine people buying some X and some Y. X is the same price but Y is more expensive. This is like the CPI going up - it now takes more money in Period 2 if you want to buy the same 10 units of X and 20 units of Y. How much more?
When we increased this agent's income, that's like the Social Security indexing to the CPI. When prices rose, we gave this person more money to compensate for the rise in prices. The intent of indexing to the CPI is to make sure people are not worse off due to rising prices (rising prices = inflation by definition, so this is what people are talking about when they mention inflation. Don't worry about it though... inflation is a macro topic you'll get in Econ 201. Just thought i'd put it here in case anyone was curious).
The 64 dollar question in part b is: We compensate by indexing to try and keep them at the same level of happiness. Is this person exactly as well off in Period 1 as in Period 2? Or is this person actually better off in Period 2 than in Period 1?