Indifference curves:
The indifferent curves defines "the combination of goods X and Y that give the consumer the same level of satisfaction", where the consumer does not have a preference of any combination of goods on the curve (Baye, 2009, 118).
The theory behind indifference curves is based on the idea that individuals can always rank any consumption bundles by order of preference (Beattie, 2006). Even though a consumer can afford a good (consumer opportunities), they will usually only purchase those goods they prefer, and their preferences are arranged in a logical order along the indifference curves.



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Figure 1: Three indifference curves on a preference map (Wikipedia)

Assumptions of Indifference curves:

1. Completeness: The consumer is able to express a preference for or indifference to certain combinations of items. All points on the indifference curve are equally preferred. The consumer is always able to make a decision.

2. More is Better: The more goods the consumer gets, the better off they are. If bundle A has the same amount of good X as bundle B, and bundle A also has more of good Y, then the consumer will prefer A to B, because they get more. The shape of the indifference curve is based on consumer preferences, and will differ among items and consumers. The slope of the indifference curve is defined by the marginal rate of substitution (MRS). MRS is the tradeoff of goods that will keep the consumer at the same level of satisfaction. If bundle A and B both lay on the same indifference curve, the MRS would be the amount of good Y the consumer gives up to gain one unit of good X, in order to stay on the same indifference curve.

3. Diminishing Marginal Utility (MU): As the consumer moves along the indifference curve, the amount of good Y they are willing to give up will decrease as they get more of good X. The MU will fall (rise) as the consumption increases (decreases), due to the substitution effect, which causes the convex shape. If a consumer decreases consumption of good X, there will be an increase of consumption for good Y for the consumer’s satisfaction to remain unchanged. The marginal rate of substitution for perfect substitution is constant and the goods have parallel lines (Beattie, 2006). The cost of giving up one more unit of Y in order to get a unit of X gets greater as you move down the indifference curve. There is diminishing MU in having too much alternatives, as each new choice subtracts from the overall satisfaction, until the marginal benefits level off (Schwartz, 2006).

4. Transitivity: Indifference curves do not intersect, so the consumer can always make a choice. The consumer can order preferences from best to worst, if bundle A is greater than bundle B, and bundle B is greater than bundle C, then it can be assumed that bundle A is greater than bundle C. The indifference curve that is farther away from the origin show a higher level of satisfaction, than curves closer to the origin (Baye, 2009).

Budget Constraints:

Budget constraints limit the consumer to selecting bundles of goods that they can afford. Consumers might prefer a certain bundle, but if it is outside of their income, then they cannot purchase it. The budget set is the combination of goods the consumer can afford and is notated as:
PxX + PyY <= M
Where M equals income and Px and Py equals the price of goods X and Y, respectively (Baye, 2009). If the consumer spends their entire income on this combination, then the budget set becomes a budget line, which exhausts the consumers’ income, and is notated as:
PxX + PyY = M
The slope of the budget line is defined as the market rate of substitution, which is the rate of which one good is traded for another in the market (Baye, 2009).


Consumer equilibrium:
Indifference curves and the budget line intersect to create consumer equilibrium, which is the consumption bundle that is affordable (within the budget line) and most satisfying to the consumer (on the indifference curve) (Baye, 2009).


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Figure 2: Consumer equilibrium (Wikipedia)


Real World Applications:

Budget Constraints:
Many poor college students deal with budget constraints everyday. Say it is Friday night, and you want to buy beer and pizza, but only have $20. The beer you prefer costs $16/case, and a slice of pizza costs $2. You are pretty hungry, and would like 3 slices of pizza, which would cost you $6. This combination would put you outside of the budget line, and you cannot afford it. So you can choose to substitute a less preferred beer at a cheaper price, or purchase less pizza, both of which would move you within the budget line. In this case, you decide to only purchase 2 slice of pizza ($4) and still get the preferred beer ($16), which would exhaust your income. With this combination, your budget line would be:
$16(1 case of beer) + $2(2 slices of pizza) = $20.

Buy One, Get One Free:
A method used by retailers to encourage consumers to purchase more is a buy one, get one free sale. For example, you are looking to purchase a new pair of shoes, and the store has a buy one, get one free (limit one free pair of shoes per customer) sign posted. You are more likely to consume more shoes than if the sale was not active. Instead of purchasing one pair of shoes at $20, you are purchasing two pairs of shoes at $20. The consumer assumes they are getting a 50% discount and the budget line is decreasing. However, this is not the case. The first pair of shoes is sold at regular price (no decrease), but the second is sold for $0. The offer does not affect the price of units below one pair of shoes or above two pairs of shoes. Using figure 1 as an example, the consumer moves from a point on L1 to a point on L2 because prior to the offer, only one pair of shoes was on the consumer’s budget line, and the buy one, get one free offer creates a horizontal budget line. The consumer purchases more with the same budget line. This technique has enticed the consumer to purchase more than he/she would have otherwise (Baye, 2009).

Gifts and Gift Certificates:
It never fails, every holiday season, you receive a gift that you are satisfied with, but if given a choice would rather have received cash or another gift instead. For example, on Christmas morning you open a present from your favorite aunt, and get a pair of socks. Inside the box is a gift receipt for $10 should you not be satisfied with the socks. You know that there is a CD at the store for $10 that you really wanted, so you choose to return the socks the day after Christmas. Using figure 1 as an example, prior to having the pair of socks valued at $10, you were sitting on L1. After receiving the gift, you automatically move to L2. When you return the socks, you now have a $10 gift certificate and can purchase the CD. This was an even exchange on the budget line but your satisfaction level is much higher. You are still on L2 because the price was the same but you shift up the line because you are more satisfied with your new gift valued at $10 (Baye, 2009). From the company perspective, issuing gift certificates reduces the amount of refunds given, and may result in consumers’ spending more than if a cash refund was given. So it is a win-win for both the consumer and the company.

Questions:
1. Which is not true of indifference curves?
a. they have a convex shape
b. they are complete
c. they intersect at the midpoint
d. MRS defines the slope of the curve
Answer: c- Indifference curves do not intersect

2. What is the equation for a budget line?

a. PxX + PyY = M
b. PyX + PxY = M
c. X + Y = PxM
d. Y = X/M
Answer: a- the budget line equation is represented by PxX + PyY = M

3. True or False: If Brian prefers pizza to tacos, tacos to hamburgers, and hamburgers to pizza, he is unable to choose the “best” kind of food because his food preferences are not transitive.
a. true
b. false
Answer: a - This is true. Brian will not be able to make a decision because his preferences have no clear order. If he is given pizza, then he would say he prefers hamburgers, and given hamburgers he would say he prefers tacos, and given tacos he would say he prefers pizza, and is back at the beginning.

4. What would Sally’s marginal rate of substitution be for beer (X) and pizza (Y) if in order to gain 1 case of beer, she would give up 2 slices of pizza, and still be equally satisfied?
a. 4
b. 3
c. ½
d. 2
Answer: d- 2. The marginal rate of substitution is equal to the slope of the indifference curve, which is rise over run, or 2/1.

5. True or False: A buy one, get one free offer gives a 50% discount on both items.
a. true
b. false
Answer: b- False. A buy one, get one free offer only discounts the second (free) item. The first item remains at regular price.



References:
Baye, M.R., (2009). Managerial economics and business strategy (6th ed.). New York: McGraw-Hill/Irwin.
Beattie, B. R. and LaFrance, J.T., (2006). The law of demand versus diminishing marginal utility. Review of Agricultural Economics, 28 (2), pg. 263-271. Retrieved October 26, 2008 from Business Source Premier database.
Consumer theory (n.d.). In Wikipedia online. Retrieved October 27, 2008 from http://en.wikipedia.org/wiki/Consumer_Theory
Indifference curves (n.d.). In Wikipedia online. Retrieved October 27, 2008 from http://en.wikipedia.org/wiki/Indifference_curve
Schwartz, B. (2006). More isn’t always better. Harvard Business Review 84(6), pg. 22. Retrieved October 25, 2008 from Business Source Premier database.