EconS 305 - Consumer Theory: Additional Topics Eric Dunaway Washington State University eric.dunaway@wsu.edu September 27, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 1 / 46
Introduction This is our last day of consumer theory. We are going to cover two applications of the income and substitution e ects. A couple notes Exam is this Friday, October 2nd! Review on Wednesday. Optional Math Review Session Today at 4 PM in Hulbert Hall room 23. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 2 / 46
Cost of Living Adjustment Let s look at an application of income and substitution e ects You are the Human Resources manager for a fast food distributor that specializes in fried chicken in New Mexico. Your boss has informed you that one of your "food scientists", Jesse, needs to be relocated from his Albuquerque location to a new facility in Mexico. For simplicity, assume that Jesse only consumes food and clothing and his utility function is Ū = x 0.5 z 0.5 where x represents food and z represents clothing. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 3 / 46
Cost of Living Adjustment Let s solve for Jesse s demand function. First, we need the marginal rate of substitution MRS = MU x = 0.5x 0.5 z 0.5 MU z 0.5x 0.5 z 0.5 = z x the budget constraint p x x + p z z = Y and the marginal rate of transformation MRT = p x p z Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 4 / 46
Cost of Living Adjustment We set the marginal rate of substitution equal to the marginal rate of transformation to obtain our tangency point MRS = MRT z p x = x p z p x x p z z = 0 And, combining this with the budget constraint is two equations and two unknowns Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 5 / 46
Cost of Living Adjustment p x x p z z = 0 p x x + p z z = Y Adding the two equations together 2p x x = Y x = Y 2p x which is our demand for food (x). Substituting this value back into the tangency point gives our demand for clothing (z), Y p x p z z = 0 2p x z = Y 2p z Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 6 / 46
Cost of Living Adjustment x = Y 2p x z = Y 2p z Jesse currently has a salary of Y = 100, and the prices of both food and clothing in Albuquerque are p x = 5 and p z = 10. Plugging these values into our demand functions yields x A = 100 2(5) = 10 z A = 100 2(10) = 5 Let s also solve for the indirect utility function. Substituting the demand functions back into the utility function gives Y 0.5 Y 0.5 Ū = = 2p x 2p z Y 2(p x p z ) 0.5 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 7 / 46
Cost of Living Adjustment Ū = Y 2(p x p z ) 0.5 We can plug in the prices and income to get Jesse s utility level in Albuquerque 100 Ū = 2(5 10) 0.5 = p 50 = 5 p 2 Now, the price for food in mexico is much higher at p 0 x = 10. The price of clothing, however, is the same, p 0 z = 10. Without any change in income, Jesse s new bundle will be x B = 100 2(10) = 5 z B = 100 2(10) = 5 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 8 / 46
Cost of Living Adjustment Your boss, who never took intermediate microeconomics, thinks the appropriate compensation for Jesse should be to give him enough income such that he could buy the same bundle as before in Albuquerque. This would amount to px 0 xa + pz 0 za = Y D 10(10) + 10(5) = Y D = 150 Thus, he thinks Jesse s income should raise from 100 to 150. Is this e cient for the rm? What would Jesse think of this deal? Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 9 / 46
Cost of Living Adjustment z 5 A 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 10 / 46
Cost of Living Adjustment z 5 B A 5 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 11 / 46
Cost of Living Adjustment z 5 B A 5 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 12 / 46
Cost of Living Adjustment z D 5 B A 5 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 13 / 46
Cost of Living Adjustment This deal works out great for Jesse, but bad for the rm. Jesse will substitute due to the di erent relative prices and achieve a higher utility level than he had even before the move. The rm is overcompensating Jesse and losing pro ts. The problem is that your boss neglected the substitution e ect. How can we x this? Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 14 / 46
Cost of Living Adjustment Instead of compensating Jesse to the point where he could a ord his original bundle, we only need to compensate him to the point where he reaches his original utility. Basically, take into account the substitution e ect and do what we have already done. We ll need the expenditure function, which we get by solving the indirect utility function for Y Ū = Y 2(p x p z ) 0.5 Y = 2(p x p z ) 0.5 Ū Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 15 / 46
Cost of Living Adjustment Y = 2(p x p z ) 0.5 Ū Recall that Jesse s original utility level was 5 p 2. Substituting this, and the new prices into the expenditure function Y = 2(10 10) 0.5 5 p 2 = 50 p 2 = 141.42 This is just over 17% less than what your boss was proposing for Jesse s compensation. Jesse is now indi erent between being sent to Mexico and staying in Albuquerque and the rm s pro ts are now higher than under the original compensation scheme. Better ask your boss for that extra 8.58 as a bonus! Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 16 / 46
Cost of Living Adjustment z 5 B C A 5 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 17 / 46
Cost of Living Adjustment Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 18 / 46
Cost of Living Adjustment As a note, the di erence between Jesse s compensation and his original income is 141.42 100 = 41.42 This is Jesse s compensating variation, because it is the amount of money Jesse has to receive after a price change to bring him back to his original utility level. We actually can see this on our gure. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 19 / 46
Cost of Living Adjustment z CV 5 B C A 5 10 x Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 20 / 46
Labor Supply Let s look at one more application of income and substitution e ects: the labor supply curve. To do this, we re going to have to adjust our model slightly. First, assume that there are 24 hours in a day (As opposed to the 37 hour Centaurian day) The consumer must choose how many of those hours to allocate to labor, H, and leisure, N. Our time constraint is then H + N = 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 21 / 46
Labor Supply Furthermore, the consumer earns income from their hours worked times a wage rate, w and an additional non-labor income, Ȳ (this could be from investments, an inheritance, food stamps, etc.). We can model this as Y = wh + Ȳ For this example, we will assume that Ȳ = 0. Lastly, the consumer gets utility from consuming good x (which requires income) and leisure. We ll leave the utility function general Ū = u(x, N) Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 22 / 46
Labor Supply x 0 A w 1 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 23 / 46
Labor Supply x B 0 A w 2 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 24 / 46
Labor Supply x C B 0 A w 3 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 25 / 46
Labor Supply Like before, we can attach another gure showing the change in wage on the vertical axis with the leisure hours on the horizontal axis. This is called the leisure demand curve. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 26 / 46
Labor Supply x C B 0 w A w3 N 24 w3 w2 w1 0 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 27 / 46
Labor Supply Intuitively, the downward sloping nature of the leisure demand curve should make sense. The wage rate is the opportunity cost of leisure, or put simpler, the price. Instead of consuming leisure, the consumer could be working and earning a wage. Thus, wage as a price for leisure is consistent. Recall our time constraint H + N = 24 We can convert this leisure demand curve into a labor supply curve using this relationship. Just take 24 minus each of the leisure values. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 28 / 46
Labor Supply w Leisure Demand w Labor Supply w 3 w 2 w 1 0 N 24 0 H 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 29 / 46
Labor Supply Leisure is a unique kind of good. Typically, it starts out inferior, then turns into a normal good. Intuitively, at rst, we need money for consumption, but as our wage rate goes up, we would rather have more free time instead of more consumption. Let s see this in action. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 30 / 46
Labor Supply x 0 A w 1 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 31 / 46
Labor Supply x B 0 A w 2 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 32 / 46
Labor Supply x B C 0 A w 3 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 33 / 46
Labor Supply w w 3 w 2 w 1 0 N 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 34 / 46
Labor Supply w w 3 w 2 w 1 0 H 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 35 / 46
Labor Supply If we calculated the income and substitution e ects for the leisure demand, we would nd that for low wages, the substitution e ect is much higher than the income e ect. This causes the consumer to respond to a wage increase by working more. As the wage increases further, eventually the income e ect overtakes the substitution e ect, causing the consumer to work less. This e ectively turns leisure into a Gi en Good. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 36 / 46
Labor Supply It is debateable whether this behavior accurately re ects reality. There is some empirical work that supports this, but it is mostly limited to the population of married women. For the most part, men and single women don t vary their labor supply or leisure demand very much with regards to their wage. However, this behavior has been seen in several high wage positions, such as doctors, professors, and CEOs. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 37 / 46
Labor Supply A consequence of the shape of this leisure demand curve is the backward bending labor supply curve. As the wage keeps going up, eventually the consumer will supply less labor to the market. If we draw a labor demand curve on top of it, we get an interesting result. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 38 / 46
Labor Supply w w 3 w 2 w 1 0 H 24 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 39 / 46
Labor Supply There are two equilibria! The equilibrium on the bottom is the one we are familiar with. The equilibrium on the top is strange. When the wage increases above the equilibrium, the market actually cannot correct itself since in this strange case, demand exceeds supply. It increases out of control and the wage just keeps going up while the consumer supplies less and less labor. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 40 / 46
Labor Supply What does this have to do with taxes? During the Reagan administration, one of his advisors drew a tax revenue curve and used it to suggest that lowering the tax rate would increase tax revenue. His argument was that lower tax rates would make people work more, and the lost revenue from the tax rate would be made up in the additional hours worked. It is called the La er Curve. It was the birth of "trickle down" economics. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 41 / 46
Labor Supply R t Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 42 / 46
Labor Supply Reagan s advisor got two things wrong. First, he picked the wrong point on the gure. We are actually on the left side, rather than the right. A later paper calculated that the optimal tax rate for maximum tax revenue is 63% (as opposed to the current 35% highest tax rate). The only country above this in the world was Denmark, and they responded by lowering taxes. Second, he didn t take into account the idea of a backward bending labor supply curve. For those who experience it, a tax cut would actually make them work less! Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 43 / 46
Summary The income and substitution e ects can be used in several real world applications to solve real world problems. Theory and empirics have to work together, though. Note: We are going to look at taxes a bit more in a week. Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 44 / 46
Preview for Wednesday/Monday Exam review on Wednesday. I will list the topics for the exam, then take questions for the rest of the period. You guys have to ask me the questions! I ll stay until we run out of time or there are no more questions. On Monday, we start Firms and Production We re done with the demand side of the market. It s time to see where supply comes from. Perlo, Chapter 6 Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 45 / 46
Assignment 3-4 and 3-5 (1 of 1) 1. Return to the cost of living example with Jesse relocating to Mexico. a. Calculate Jesse s intermediate bundle (Point C) b. Calculate the total e ect c. Calculate the substitution e ect d. Calculate the income e ect Eric Dunaway (WSU) EconS 305 - Lecture 8 September 27, 2015 46 / 46