Tuesday, January 17, 2006

Intuition behind income and substitution effects

Okay, so you guys really don't like the income and substitution effect diagrams. I feel your pain, I really do. (see p. 467 in textbook) I want to try again to explain intuitively what is happening. You can break down the pivot of the budget line (as a result of a price change) into two steps: a slope rotation and a shift. The slope rotation is the substitution effect and the shift is the income effect. Say you start at an optimum A, as in the text, and the price of the good on the y axis decreases. For the substitution effect, you will consume more of good Y and less of good X. (everything I say is the opposite in the case of a price increase) Your utility will not change, so you will stay in the same indifference curve. How do you draw this? Find the point on the original indifference curve that has a slope equal to the new price ratio. This is your point B. Now draw a line tangent to it. This is your intermediate budget constraint. Intuitively, this is the point you would consume at if I took just enough money away from you such that the best you could do was to stay on your original indifference curve. Now, the income effect is what happens when I give you this money back. Thus it is a parallel shift of the intermediate budget constraint. (shift out with a price decrease, shift in with a price increase) To where? It shifts such that the new budget constraint touches the x axis at the same point as the old budget constraint. Now you can label an appropriate point C (depending on whether goods are normal or inferior), draw an indifference curve tangent to C, and you've found your new optimum.

Income Distribution

Why does no one seem to remember that we did a section on Income Distribution? We went over Lorenz curves and Gini coefficients at the review, but there is more material in the helpful hint on Income Distribution. Some questions I received on this material:

Q: Is poverty rate calculated in terms of people or households?

A: It is calculated in terms of people, which is different from how we calculate quantiles and such.

Q: Is the poverty gap the total amount of money required to get out of poverty or the average amount per person?

A: It is the total amount.

Read Chapter 21...

...which is on budget constraints and indiffernce curves. I feel like we did not review enough of this. Also, read the green boxes in the text. The review material that goes along with this are the diagrams and equations that I gave you relating to the slope of budget constraints and indifference curves and such.

Lecture material

Just a reminder that lecture material is testable, even if it is not covered in the textbook!

Demand for Labor

Okay, some useful facts about labor demand:

-- marginal product of labor (MPL): how much an additional laborer adds to quantity produced

-- marginal revenue product of labor (MRPL): how much in dollar terms an additional laborer adds to the firm; equals output price times marginal product, therefore changes with either output price changes or marginal product changes; also called the value of the marginal product

-- firms will demand labor up until the point where the MRPL equals the wage

Suggestions on Textbook Readings

I suggest that you look at the graphs and explanations for the following sections in the textbook, since they are important but were not (in my opinion) sufficiently covered in the reviews.

-- income and substitution effects: Figure 9 on p. 465 (also figure 10 on p. 467

-- supply of labor: Figure 14 on p. 471

-- supply of saving (capital) Figure 16 on p. 474

-- Demand for Capital: Figure 7 on p. 405

-- Demand for Labor: Figure 3 on p. 396

The discussion on pp. 397-398 is also helpful.

Comparative Advantage Caveat

In case this wasn't mathematically obvious, you can't have comparative advantage in more than one good in a two good scenario. If country A has comparative advantage in good X, then country B has comparative advantage in good Y. However, there can be a case in which neither country has any comparative advantage if the opportunity costs are the same in both countries. In this case there are no potential gains from trade.

Ricardo's Difficult Idea

A number of you have mentioned that you didn't understand the article "Ricardo's Difficult Idea". I have the article in front of me, and I don't specifically know what would be helpful to tell you about it. I would say just to read it carefully and try to remember as much as you can. If you have specific questions, please email and let me know and I will post the answers here.

Giffen Goods

Most of you remember Giffen goods as goods that have upward sloping demand curves. However, it is also important to remember that these goods are in fact inferior goods. You can think of them as VERY inferior goods, since they are inferior goods where the income effect outweighs the substitution effect, which is how you get the upward slope in the demand curve.

Income and Substitution Effects


How do I know when I need to talk about the income and substitution effects?


Generally, you need to think about income and substitution effects when thinking about changes in consumption. This could be a price change of a good, a change in wage (if talking about supply of labor and consumption of leisure), or change in interest rate (if talking about supply of capital and consumption in year 1).

If a problem asks about change in consumption as a result of change in income, you need to only consider the income effect.

Public and Private Goods


One quick question about public goods. A few times throughout the solutions to the practice problems, it is stated that public goods are not required to be non-excludable, but merely need low-rivalry.
However, the book and my section notes tell me otherwise (that both are required). Which is correct?

Go with what is in the section notes and the book. As a refresher:

Private goods: excludable and rival

Public goods: neither excludable nor rivel

Common resources: rival but not excludable

Natural monopoly: excludable but not rival

Saturday, January 14, 2006

Unit 2 Practice Problem #5


I was doing the practice problems for unit 2 that are posted on the course website, and I ran into some confusion regarding interest rates and budget constraints. For #5, the budget constraint has consumption in the first year on the x-axis and consumption in the second year on the y-axis, as expected. However, the consumption in the second year does not account for the money that will additionally be earned in that year; in other words, the maximum consumption is 31500, from the money saved from the first year, instead of 30000 + 31500, using the money saved from the first year in addition to the money gained in the second year. However, as I recall, there was a similar problem in PS6 that followed the second way. What should I do, should this problem arise on the exam?


You are right about the practice problem. As far as the exam goes, your best bet is to just state any assumptions that you make. In this case, I would say something like "I am assuming that I get $30,000 both this year and next year and I can't borrow any money".

Also, note that the way the practice problems are labeled by unit corresponds to what unit they were in last year, not this year. Obviously, budget constraints and indifference curves were not covered in unit 2 this year for example!

Friday, January 13, 2006

Cross-Price Elasticities

Note: you don't need to know this for the purposes of Ec10.

A question was asked about cross-price elasticities at the review session yesterday. Basically, cross price elasticities just measure the degree to which two goods are substitutes or complements. In other words, a cross-price elasticity is of the form:

% change in quantity demanded of good B/% change in price of good A

So this number would be positive for substitutes and negative for complements.

If you are curious, you can find more information here.

Deriving the MR curve

Q: How do I derive the MR curve from the demand curve?

A: In class, we said that the marginal revenue curve was twice as steep as the demand curve. Remember that slope of the demand curve is change in P/change in Q. Also, the demand curve and the marginal revenue curve will have the same intercept on the price axis. Here is an example:

if we have demand as P=40-2Q, then we will have marginal revenue as P=40-4Q. (Remember that this works only when you solve for P in your demand equation.)

Again, you don't NEED to know this for EC10, but...why does this work?

So, total revenue = price times quantity. So, using the above example:
TR = PQ = (40-2Q)Q = 40Q-2Q^2

As mentioned before, marginal revenue is the derivative of total revenue. Hence:
MR = 40-4Q. Just as above! You can see from the structure of the problem why this would always be the case.

For those of you mathy people out there...

Note: you don't have to know this for the purposes of Ec10.

For those of you that haven't already figured this out, when we talk about marginal something- marginal cost, marginal revenue, etc.- for continuous functions we are technically referring to the derivatives of total cost, total revenue, etc. respectively. For example, we define MC as change in cost over change in quantity, but this is easily extended to the case where change in quantity is very small, and we can dTC/dq.

This helps to explain why, for example, we maximize total revenue by setting marginal revenue equal to zero, since if you were to just think about it outside of Ec10, you would take the derivative of TR and set it equal to zero.

That said, try not to use things you are not supposed to know on your exam, but think about them to help you decide how to approach a problem. :)