MICROECONOMIC THEORY 1 Lecture 2: Ordinal Utility Approach To Demand Theory Lecturer: Dr. Priscilla T Baffour; ptbaffour@ug.edu.gh 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 1
Content Assumptions Curvature of indifference curves Impossible indifference curves Satiation Monotonic Preferences The budget Constraint Consumer equilibrium 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 2
Assumptions The consumer is rational Ordinal utility-the consumer ranks his preferences based on satisfaction derived from each good. Total utility depends on quantity consumed Consistency and transitivity of choice Diminishing marginal rate of substitution IC is convex to the origin Slope of IC decreases 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 3
Indifference Curve IC is the locus of points-bundle of goods- that yield the same level of satisfaction. An indifference curve defines the substitution between goods X and Y that is acceptable in the mind of the consumer. Indifference map shows all ICs which rank the consumer s preference. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 4
Indifference Curve IC is convex to the origin. The convex shape indicates as you move towards the southeast along a typical IC, the consumer gives up less and less of Y for an extra unit of X. In other words what is sacrificed for an extra unit of X diminishes. The negative of the slope of IC is the marginal rate of substitution. The rate of substitution declines along an IC (diminishing marginal rate of substitution) 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 5
Indifference Curve 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 6
Second order condition Essentially ensures that the utility curve is convex. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 7
Impossible Indifference Curves B Burritos, per semester e a b I 1 I 0 Lisa is indifferent between e and a, and also between e and b so by transitivity she should also be indifferent between a and b but this is impossible, since b must be preferred to a given it has more of both goods. Z, Pizzas per semester 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 8
B, Bur r itos per semester Impossible Indifference Curves (cont.) Lisa is indifferent between b and a since both points are on the same indifference curve But this contradicts the more is better assumption. Can you tell why? Yes, b has more of both and hence it should be preferred over a. I a b Z, Pizzas per semester 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 9
Figure 4.2 Impossible Indifference Curves 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 10
Curvature of Indifference Curves Casual observation suggests that most people s indifference curves are convex. Special Cases: Perfect substitutes - goods that a consumer is completely indifferent as to which to consume. Perfect complements - goods that a consumer is interested in consuming only in fixed proportions. 2017/18 11 Priscilla T. Baffour (PhD) Microeconomics 1
Figure 4.4(a): Perfect Substitutes Co k e, Cans per w eek 4 3 2 1 I 1 I 2 I 3 I 4 Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like? Straight, parallel lines with an MRS (slope) of 1. Bill is willing to exchange one can of Coke for one can of Pepsi. 0 1 2 3 4 P epsi, Cans per w eek 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 12
Figure 4.4(b): Perfect Complements Ice cream, Scoops per w eek 3 2 1 e d a b c I 3 I 2 I 1 If she has only one piece of pie, she gets as much pleasure from it and one scoop of ice cream, a, as from it and two scoops, d, or as from it and three scoops, e. 0 1 2 3 Pi e, Slices per w eek 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 13
Bads A commodity the consumer doesn t like. Noise Sleep 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 14
Neutrals The consumer doesn t care about it in one way or the other Noise Sleep 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 15
Satiation A situation where there is some overall best bundle (x 1, x 2 ) for the consumer, and the closer she is to that bundle, the better off she is in terms of her own preferences. In this scenario ICs have a negative slope when the consumer has too little or too much of both goods and a positive slope when he has too much of one of the goods. Having too much of one of the goods makes it a bad, reducing the consumption of the bad good moves her closer to the bliss point If she has too much of both goods, they both become bads, so reducing the consumption of both moves her closer to her bliss point 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 16
Satiated Preferences 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 17
Monotonic Preference Premised on the idea that more is better, and that, we are examining conditions before the consumer reaches a satiation point. Monotonicity implies that indifference curves have a negative slope. Averages are preferred to extremes. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 18
Monotonic Preference More of both goods is better for this consumer X2 Better bundles Worse bundles X1 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 19
Budget Constraint Budget line (or budget constraint) - the bundles of goods that can be bought if the entire budget is spent on those goods at given prices. Opportunity set - all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 20
Budget Constraint (cont.) If Lisa spends all her budget, Y, on pizza and burgers, then p B B + p Z Z = Y where p B B is the amount she spends on burgers and p Z Z is the amount she spends on pizzas. This equation is her budget constraint. It shows that her expenditures on burgers and pizza use up her entire budget. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 21
Budget Constraint (cont.) How many burgers can Lisa buy? To answer solve budget constraint for B (quantity of burgers): B Z Z B Z B P Z P Y B Z P Y B P Y Z P B P 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 22
Budget Constraint (cont.) From previous slide we have: B Y P P B Z Z If p Z = $1, p B = $2, and Y = $50, then: B $50 ($1 Z) 25 0.5Z $2 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 23
, B Burgers per semester Figure 4.7: Budget Constraint 25 = Y / p B 20 a Amount of Burgers consumed if all income is allocated for Burritos. b L 1 From previous slide we have that if: p Z = $1, p B = $2, and Y = $50, then the budget constraint, L 1, is: $50 ($1 Z) B 25 0.5Z $2 10 Opportunity set c Amount of Pizza consumed if all income is allocated for Pizza. 0 10 30 d 50 = Y / p Z Z, Pizzas per semester 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 24
Figure 4.8(a) Changes in the Budget Constraint: Price of Pizza Doubles B, Burgers r per semester 25 0 Slope = -$1/$2 = -0.5 L 2 (p Z = $2) Slope = -$2/$2 = -1 L 1 ( p Z = $1) Loss 25 B = 50 Z, Pizzas per semester Y P B - P Z = $1 $2 P B Z If the price of pizza doubles, (increases from $1 to $2) the slope of the budget line increases This area represents the bundles she can no longer afford 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 25
B, Burritos per semester Figure 4.8(b): Changes in the Budget Constraint: Income Doubles B = $100 $50 - P B P Z P B Z 50 L 3 ( Y = $100) If Lisa s income increases by $50 the budget line shifts to the right (with the same slope!) 25 L 1 ( Y = $50) Gain This area represents the new consumption bundles she can now afford!!! 0 50 100 Z, Pizzas per semester 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 26
Consumer equilibrium The consumer maximizes utility at a point where the slope of the indifference curve (MRS) is equal to the slope of the budget constraint. At the chosen point we have tangency of the indifference curve and the budget constraint, px/py = MRS = MUx/MUy, i.e., MUx/px = MUy/py. 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 27
Figure 4.9 Consumer Maximization, Interior Solution (cont.) B, Bur r itos per semester 25 The budget constraint and the indifference curve have the same slope at the point e where they touch. Therefore, at point e: e MRS MU MU Z B Slope of I 2 P P Z B Slope of BL MRT I 2 0 50 Z, Pizzas per semester 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 28
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Corner solution: Boundary-optimal solution with only commodity x 2 being consumed 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 30
Corner solution for perfect substitutes 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 31
Corner solution with strictly concave preferences 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 32
Recap on Taxes, Subsidies & Rationing Forms of Taxes 1. Quantity (specific) tax 2. Ad valorem (value) tax 3. Lump sum tax Forms of Subsidies Specific subsidy Ad valorem Lump sum Rationing 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 33
Problem A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer s opportunity set change? 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 34
Solved Problem 2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 35