Micro101 - Topic 7 - Consumer Equilibrium-1 PDF

Principles of Microeconomics Econ101 Topic 7 Consumer Equilibrium -1  Utility Utility is the total satisfaction received from consuming a good or a service Supply and demand and price arise out of the basic problem of scarcity Scarcity causes ec...

Principles of Microeconomics Econ101 Topic 7 Consumer Equilibrium -1  Utility Utility is the total satisfaction received from consuming a good or a service Supply and demand and price arise out of the basic problem of scarcity Scarcity causes economics and the market to allocate resources efficiently – Only the market is efficient. Governments interfere at their peril! Utility explains how individuals and societies gain optimal satisfaction in dealing with scarcity  Utility Theory The more pleasure (satisfaction, utility) we get from a product, the higher the price we’re willing to pay for it. – Utility: the pleasure or satisfaction obtained from using a good or service. – Total utility: the amount of satisfaction obtained from the consumption of a series of products. – Marginal utility: the change in total utility obtained by consuming one additional (marginal) unit of a product.  Total and Marginal Utility Utility is an abstract concept rather than a tangible measurable quantity Cardinal utility assigns numbers to utility (not used much) Ordinal utility talks in relative terms In general, a person’s total utility is a function of the the level of consumption – More you consume, more total utility you get Marginal utility is the additional utility or satisfaction gained from an extra unit of consumption As usual, we are more interested in marginal utility than in total utility  Total and Marginal Utility Total Utility (TU) increases as more of a good is consumed but Marginal Utility (MU) usually decreases as consumption of a good increases Thus, the Law of Diminishing Marginal Utility Chocolate Bars Total Utility Marginal Utility Eaten from chocolate from Chocolate 0 0 0 1 70 70 2 80 10 3 85 5 4 88 3  Diminishing Marginal Utility The Law of Diminishing Marginal Utility helps explain the Law of Demand and downward sloping demand curves Rationality is important Consumers will not go on endlessly eating chocolate bars Instead of spending their money on 3 chocolate bars with a TU of 85, consumers may buy one chocolate bar with a TU of 70 and a glass of milk to go with it which as a TU of 50 This combination gives the consumer a TU of 120 at the same price as 3 bars of chocolate  Diminishing Marginal Utility Law of diminishing marginal utility: the marginal utility of a good declines as more of it is consumed over a given time period. – The pleasure received from the next slice of pizza, say, is less than the pleasure received from the previous slice. Eventually, additional quantities of a good yield smaller increments of satisfaction.  Diminishing Marginal Utility As long as marginal utility > 0, total utility increases. When marginal utility becomes negative, total utility maxes out and then decreases.  Utility Function In the case of 2 goods, Q1 and Q2, consumer’s utility function is U = f (q1,q2) Where q1 and q2 and the quantities consumed of the two goods Q1 and Q2 Different combinations of quantities of the two goods are seen to give us the same level of utility When we plot these sets of points where different combinations of two goods yield the same utility, we get an indifference curve (IC)  Indifference Curves Indifference curve: a curve depicting alternative combinations of goods that yield equal satisfaction. – This is a mechanism for illustrating consumer preferences. – It can be used as a basis from which to construct a demand curve.  Indifference Curve Map Every consumer can be said to possess an indifference curve map This shows indifference curves at different levels of utility Each higher curve represents a higher level of utility But along a curve, the consumer is indifferent to different combinations of goods.  Properties of Indifference Curves Completeness – For 2 goods A and B, we either prefers A to B or prefers B to A or we’re indifferent between the two Transitivity – When looking at three bundles of goods A, B, C, if we prefer A to B and B to C, then we prefer A to C. Similarly, if we are indifferent between A and B, and indifferent between B and C, then we are indifferent between A and C Non-satiation – Ceteris paribus, the consumer always prefers more goods to less goods Convexity – The rate at which we are willing to give up one good in exchange for another good, while remaining indifferent after the exchange, DECREASES as we get more of the 2nd good and less of the first good  Properties of ICs ICs are always downward sloping and convex to the origin and cannot ever intersect This cannot happen  Marginal Rate of Substitution We have not assumed anything about the curvature of ICs or the slope of the IC. The Marginal Rate of Substitution (MRS) is the rate at which a consumer gives up one good for more of the other good while remaining at the same level of satisfaction or remaining indifferent to the new combination Marginal Rate of Substitution  MRS As the consumer moves further down the IC, MRS decreases This is the Law of Diminishing Marginal Rate of Substitution The slope of the IC is continuously decreasing MRS is the slope of the curve As you move down the IC, marginal utility of one good declines while the MU of the other good increases But overall utility remains the same But that is why ICs are convex to the origin  Consumer Equilibrium We know that the consumer is indifferent to various combinations of two goods as long as the consumer remains on the same IC So, what prevents the consumer from reaching higher and higher ICs on the IC map? Answer: Income or budget Plus the prices of the two goods When all this is put together, we can see what equilibrium looks like Take a stepwise approach  Budget Constraint Also called a Consumption Possibilities Frontier  Budget Constraint All possible combinations of two goods (Beans and Rice), given prices and a budget (income) Assume a can of beans costs $6 and a serving of rice costs $4 Consumer’s income is $48 If he spent his entire income (budget) on beans, he could buy 8 cans of beans If he spent his entire income on rice, he would get 12 servings of rice But he is a rational consumer. He wants both rice and beans Hence, he will look for some combination along the BC  Slope of the Budget Constraint The slope of the BC is the ratio of the prices of the two goods Slope = Price of good Y/Price of good X Equation of the BC is PxQx + PyQy = Y (income)  Bringing it Together - Equilibrium ICs indicate what consumers are willing to buy BC shows what the consumer is able to buy When we combine the BC with an IC we find quantities of each good that the consumer is both willing and able to buy We superimpose an indifference curve map on the consumer’s BC The rational utility maximizing consumer will select a combination along the BC that lies on the highest indifference curve possible Consumer maximizes utility given his budget constraint  Consumer Equilibrium Where the BC is just tangent to the highest possible IC  Consumer Equilibrium Consumer equilibrium occurs when Slope of the IC = Slope of the BC There is only one unique point where this happens Slope of the IC is the MRS Slope of the BC = Price Ratio of the two goods So, MRS = PB / PR Equation of the Budget Constraint is Pb.Qb + Pr.Qr = Y (income) Slope of the BC is the negative of the price ratio of the two goods  Consumer Equilibrium Consider a small movement down an IC The additional consumption of good X, ∆x, will generate some amount of marginal utility MUx and a total utility increase of MUx.∆x. At the same time, the reduced consumption of good Y, will generate a loss of marginal utility MUy and a total loss of utility of MUy.∆y. But since the level of total utility on the same IC is always the same, the total gain in utility of X must equal the total loss of utility in Y 0 = MUx(∆x) + MUy(∆y) or -(∆y/∆x) = MUx/MUy  Consumer Equilibrium But –(∆y/∆x) is the slope of the indifference curve Or MRS of Y for X Thus MRS = MUx/MUy But we have seen that at the point of equilibrium, the slope of the IC and BC are equal And the slope of the BC is the price ratio of the two goods MUx/MUy = Px/Py Or MUx/Px = MUy/Py Consumer equilibrium implies that the marginal utility per dollar of expenditure is the same for each good.  Problem 1 Mr Wang uses his income to purchase shawarmas and candy. The price of a shawarma is $6. He can purchases 45 shawarmas with all his income or 90 pieces of candy with all his income. Income? Price of Candy? Show his consumer equilibrium (roughly). When the Price of One Good Changes  Price Consumption Curve A curve or line drawn through the various points of consumer equilibrium as prices changes and the BC shifts When the Price of Both Goods Change New BC  Increase in Consumer’s Income New BCs represent a change in consumer’s income  Changes in Income First step: BC shifts outwards. New equilibrium reached on highest IC  Income Consumption Curve A curve or line drawn through the various points of consumer equilibrium as a consumer’s income increases and the BC shifts outwards  Deriving a Demand Curve From the PCC The Price Effect  Price Effect Price Effect is seem when the price of (usually) one good changes while income is constant The price effect is a combination of two effects – The subsitution effect – The income effect The substitution effect is ALWAYS positive and is depicted as a movement along the initial IC The income effect could be positive or negative depending on the good and is depicted as a movement to a new indifference curve  Price Effect The substitution effect involves the substitution of one good for another due to a change in the relative prices of the two goods This means a movement along the same IC to a new MRS position The income effect results from an increase or decrease in the consumer’s real income or purchasing power as a result of the price change This means a movement to a new lower or higher IC The sum of these 2 effects is the Price Effect Price Effect for a Normal Good B A C  Two Effects at Work Whenever there is a fall in price of one product, the budget constraint rotates outwards and the consumer buys more of the product whose price has fallen There are two effects at work here – the substitution effect and the income effect Substitution effect is a movement along the same indifference curve to a point with a different MRS – Consumer gives up one good for more of another good whose price has fallen but remains at the same level of utility (IC) Income effect is a shift to new higher indifference curve – Real income effect makes consumer buy more of both goods – more utility and higher indifference curve and shift to a higher IC The net price effect is the sum of these two effects  Problem 1 Maddy is currently using all her income on milk at $4 per unit and on fish at $15 per unit. The MU of the next unit of milk is 40 utils and the MU of the next unit of fish is 105 utils. How can Maddy rearrange her consumption to maximise utility? Use the condition of consumer equilibrium: MU/$ is equal for both goods. MU/$ for milk is 40/4 = 10 utils/$ MU/$ for fish is 105/15 = 7 utils/$ Since 10>7, Maddy should spend more of her income on milk and less on fish.  Problem 2 Mr Wang uses his income to purchase shawarmas and candy. The price of a shawarma is $6. He can purchases 45 shawarmas with all his income or 90 pieces of candy with all his income. Income? Price of Candy? Show his equilibrium (roughly). Price of shawarma rises to $9. Show what happens to his equilibrium. Income increases by $30. Show his net equilibrium position. More Practice Problems ECON 101  If the elasticity of demand for college textbooks is 0.1, and the price of textbooks increases by 20%, how much will the quantity demanded change, and in what direction? What is the equilibrium price and quantity of milk? * a. price: $4; quantity: 4500 b. price: $3; quantity: 3500 c. price: $2, quantity: 2000 d. Indeterminate from the information given.  If in the previous question the government imposes a price maximum of $2: Is this a price ceiling or price floor? Why? Is there a shortage or a surplus of milk? By how many units? What is the MU of consuming 5th the slice of pizza? Which slice of pizza give the consumer the highest MU?