ECN 104 Notes MARCH 10-14 Elasticities and Taxes When the government puts a tax on the sellers (i.e. manufacturing tax), the tax can be viewed as an increase in the firm s marginal cost. But who is really paying for the tax? It depends. Ex/ $1 tax on wine Price of Wine ($) St S 4.50 4.00 3.50 Tax of $1 D Quantity of wine Before tax, consumers paid $4/bottle. After tax consumers pay $4.50/bottle. Before tax, suppliers earned $4/bottle. After tax suppliers earned $3.50/bottle. So the burden of the tax falls equally on consumers and producers. (each pay 50% of the tax). 4.50-4=0.50, 4-3.50=0.50 Is the burden of the tax always equally divided? No, it depends on the elasticity of demand and elasticity of supply. The more sensitive demand is to price (the higher the elasticity), the smaller the portion of the burden falls to consumers. Some examples: 1. Very elastic demand, moderately elastic supply => most of the tax burden is paid by the suppliers. Price St S Consumer s share Producer s share D
2. Inelastic demand and moderately elastic supply => most of the tax burden is paid by consumers. Price St S Consumer s share Producer s share D Quantity Government Set Prices Price Ceiling a legal maximum price for a good/service Ex/ Oil price capped at 1.50/litre What happens if there is a price ceiling in the market? price There will be a shortage of the good. S How will the gov t ration who should get the limited goods when there aren t enough P e to meet demand? Usually a black market crops up (people pay more under the table) P f D In the long run, supply becomes less elastic shortage Why? Lower Price -> lower profit -> fewer Producers Qs Qd Q Price Floor a legal maximum price for a good/service Ex/ minimum wages What happens if there is a price floor in the market? There will be a surplus of the labour (unemployment). price S P e P f D shortage Qs Qd Q
Chapter 7 Consumer Choice Recall again the law of demand. As Price falls, quantity demanded increases. We can explain this result in several ways. Each interrelated. Income effect- as price falls the purchasing power of income rises, thereby causing demand to rise. Substitution effect- as the price of good A falls, good A becomes relatively less expensive compared to other goods, so good A becomes more attractive to consumers, and demand for good A rises. Law of Diminishing Marginal Utility As quantity consumed increases, the marginal utility (MU) obtained from each additional unit falls. With your first winter coat, your marginal utility is very high (without a coat you freeze) A second winter coat brings a lot of utility, because it s nice to have a change, while one coat is at the cleaners you can still go out without freezing. By the 9 th or 10 th winter coat, each extra coat brings little or no utility. In fact, it might bring negative utility because the extra coats just hang in your closet and take up space. Thus as # of coats increases, the marginal utility from the extra coat decreases. Since you are willing to buy MU with dollars, this is the same as the law of demand. As price increases quantity demanded decreases. NOTE: Utility = units of happiness. This is a subjective term and is difficult to quantify because no two people will measure alike. Hence, what is important is one person s ordering of utility and preferences. Total Utility versus Marginal Utility Total Utility = the total amount of satisfaction obtained from the consumption of a good or set of goods. (note: total utility= sum of marginal utilities for each unit included in the set of goods) Marginal Utility = the extra utility obtained from the consumption of one additional unit of a good : MU= change in TU / change in Q Note: the amount by which MU decreases, with an increase in units consumed, depends on the products price elasticity of demand. C.P., if MU decreases by a lot with each extra unit, then demand is relatively inelastic.
Definitions to keep in mind: Rational Behavior - rational people use their incomes to obtain the greatest amount of utility possible. (if a person uses all of their income to obtain less than the highest possible utility, they are said to not behave rationally) Preferences each person knows which goods they prefer over others. Ex/ Jane: apples>oranges>grapefruits, Joe: oranges>apples>grapefruits We also assume they know how much utility/happiness they would get from each unit of each good. Budget constraint each person has a fixed, limited amount of $ they can spend. This is called a budget. Prices Goods each have a set price that is fixed and does not vary with one person s purchases Consumer Decision Making Every person has their own decision to make as to what amounts of what goods they will purchase with their limited budget If the person has made a decision and would not improve their happiness by altering it, this is the equilibrium decision for that person. How do they determine this? Utility Maximization Rule Consumers should allocate their money income so as to maximize total utility given their budget. They do this by allocating their money income so that the last dollar spent on each product yields the same amount of marginal (extra) utility. Marginal Utility per Dollar If different goods cost different amounts, we cannot simply compare their marginal utilities, but rather we must look at the marginal utility per dollar spent on each good. EX/ if granola costs $4 and yields 4 util and corn flakes cost $3 and yield 1 util, I d clearly be better off buying granola, even though it is more expensive. I can only know which is better if I look at utils per dollar.
Example of How to Maximize Utility: Suppose Jane has the following marginal utility from Apples and Breadsticks: Unit of Products Apples ($1/ea) Breadsticks ($2/ea) MU MU/$ MU MU/$ 1 st 10 10 24 12 2 nd 8 8 20 10 3 rd 7 7 18 9 4 th 6 6 16 8 5 th 5 5 12 6 6 th 4 4 6 3 7 th 3 3 4 2 8 th 2 2 2 1 Suppose Jane has $10 to spend. How should she spend her money? She should spend it in a way such that she gets maximum satisfaction. According to our rule above, she should spend it until all money is gone and the last dollar spent on each good yields the same marginal utility. That is, at 2 apples and 4 breadsticks. Let s consider her decision process. Her first choice is between 1 apple and 1 breadstick. Since the latter yields more MU per dollar, she buys 1 breadstick. She has $8 left Her second choice is between 1 apple and 2 nd breadstick. Since they both yield the same MU per dollar, she buys both. She has $5 left Her second choice is between 2 nd apple and 3 rd breadstick. Since the latter yields higher MU per dollar, she buys breadstick. She has $3 left Her second choice is between 2 nd apple and 4 th breadstick. Since they both yield the same MU per dollar, she buys both. She has $0 left. So Jane s total utility is 96, with 4 breadsticks and 2 apples. She could have bought another combination of these goods, but no other combination would yield higher utility for Jane for $10. Test it out and see. We can restate our utility maximization rule in a format that is easy to remember: Utility is Maximized where: MUa = Mub Pa Pb and all income is spent
Utility maximization and the demand curve What happens if the price of breadsticks falls to $1? We can redraw the chart above: Unit of Products Apples ($1/ea) Breadsticks ($1/ea) MU MU/$ MU MU/$ 1 st 10 10 24 24 2 nd 8 8 20 20 3 rd 7 7 18 18 4 th 6 6 16 16 5 th 5 5 12 12 6 th 4 4 6 6 7 th 3 3 4 4 8 th 2 2 2 2 Now, Jane will maximize her utility at 6 breadsticks and 4 apples. So we see that we can derive a single consumer s demand schedule for breadsticks by determining how many she will buy at different prices. Price $2 $1 Jane s Demand for breadsticks 4 6 Quantity Notice that Jane s demand (and anyone elses) depends on preferences/tastes (as measured by utility), income ($10) and prices of other goods (apples-$1)
Income versus Substitution Effects: Substitution: in our example, the price of breadsticks falls from $2 to $1 At $2 : At $1 : MUa(8)/Pa(1) = Mub(16)/Pb(2) MUa(8)/Pa(1) < Mub(16)/Pb(1) Therefore, after the price fell, we d increase our total utility if we bought more breadsticks relative to apples. -> substitute more of B over A (demand for B increases) Income Effect: Before the price of B fell, Jane had spent all her money to purchase 4 breadsticks and 2 apples. After the price fell, Jane would have had $4 left over after buying 4B and 2A. Thus, her real income is greater when Pb falls, and she can purchase more (demand increases) Real income how much you can purchase with your income Money income how many $ you have to spend Value of Time Consumption and production take time. Time is valuable because we can work and earn money to buy goods, or/and we can enjoy ourselves (leisure) and get utility directly. By spending an hour in leisure or consumption, you forgo an hours wages. Consider: Playing golf - cost= 4hrs + $30 Going to concert - cost= 2hrs +$80 If you make $10 hour, which is more costly? Concert = $100 > Golf = $70 If you make $100/hr, however, Golf becomes more costly. $430>$280
Appendix A more advanced look at consumer decision making follows: Budget Line this line shows the various combinations of 2 goods which a consumer can purchase with a given budget. Ex/ in Jane s case, where her budget was $10 and the price of apples was $1 and the price of breadsticks was $2. If she buys only apples, the most she can buy is 10. If she buys only breadsticks, the most she can buy is 5. Her budget line is this: Q Apples 10 Budget Line. The slope of this line is: Slope = Pb/Pa = 1/2 5 Q Breadsticks What happens if total income changes? The budget line will shift in or out depending on the change. Ex/ if Jane has 20 dollar budget, her line will shift out parallelly. Q Apples 20 10 New Budget Line. The slope of this line is: Slope = Pb/Pa = 1/2 5 10 Q Breadsticks
What happens if the price of bread sticks drops to $1? The budget line will swivel. Recall that the slope of the budget line is Pb/Pa Q Apples 10 New Budget Line. The slope of this line is: Slope = Pb/Pa =1 5 10 Q breadsticks Now if she spent all her money on breadsticks, she could buy twice as many. But if she spent all her money on apples, she d still only be able to buy 10. Indifference Curves curves showing different combinations (of two goods) that yield the same total utility. An indifference curve is a curve which shows different combos of 2 goods where the consumer is indifferent between the combos. Ex/ I have a basket of 10 utility. The possible goods it contains to give 10 utils are (4A+1B, 2A+2B, 1A+4B) I don t care which combination is in the basket. No matter what I will be equally happy. Qa 4 2 1 X Io (utility=10) 1 2 4 Qb
The slope of an indifference curve is the Marginal Rate of Substitution (MRS) MRS= rate at which the consumer is prepared to give substitute one unit of B for one unit of A = MUb/MUa This curve is downward sloping because more of one product means we must consume less of another if the Total Utility is to remain constant. What would happen if we were to consume at point X? We d have a higher level of utility (total utility>10) Indifference curves are bowed inward to the origin. Why? Because as we move along the curve, we are getting more and more B. The more B we have, the LESS we are willing to substitute B for A, therefore the lower our MRS, therefore the less steep our slope, therefore the curve is convex or bowed inward to the origin. Suppose we have the following MU table for Bob: Unit # MUa Mub 1 8 6 2 6 4 3 3 3 4 1 2 5 0 1 4A + 1B = 24 Utils 2A + 2B = 24 Utils 1A + 5B = 24 Utils Each of these combinations are on the same utility cuve Qa 4 2 1 Io (utility=24) 1 2 5 Qb
Suppose you have $6 and the price of A is $2.00 and the price of B is $1. What is the budget line? Qa 2.5 Slope=1/1.5 1 2 5 Qb What combination of goods yields the maximum utility? The optimal utility is found where an indifference curve is just tangent to the budget line. This is where all the budget is spend, and where MUb/Pb = MUa/Pa. Note: this is the same condition as: MUb/MUa = Pb/Pa, which means the slope of the budget line equals the slope of the Indifference curve. So we see equilibrium is where they are tangent: Qa 2.5 2 Io (utility=24) 2 5 Qb The equilibrium is at the tangency marked by the star. Why is the equilibrium at this tangency point and not at some other point on the budget line? Because any other point on the budget line will have a lower total utility, therefore it is not optimal.
Note: a single indifference curve shows some constant utility. But we can sketch a whole set of indifference curves. A set of curves is called an indifference map. Qa Utility increases as we move away from the origin 2 I 4 (total utility=30) I 3 (total utility=28) 2 5 Qb Equilibrium position is that combination of products that yields the greatest utility given our budget. Derived demand curve As before, we can use price and utility information to derive a single consumer s demand. Suppose that the price of A falls to $1. What will be our new demand for A? It will be 3. Qa 5 3 3 5 Qb Io (utility=24)