EconS Income E ects
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1 EconS Income E ects Eric Dunaway Washington State University eric.dunaway@wsu.edu September 23, 2015 Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
2 Introduction Over the net two lectures, we are going to talk about how our equilibria that we found vary with changes in income and prices. But rst. We call this the income and substitution e ects. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
3 Econ in the News I d like to talk about an interesting news story soaring through the internet the last few days. Some background: Daraprim, a medication commonly used by HIV patients to ght o a parasitic infection has been on the market for 62 years for the price of $ $18 per pill. Recently, a venture capitalist named Martin Shkreli purchased the rights to Daraprim, and raised the price immediately to $750 per pill. Economically, why would he do this? Is this fair? Should the government intervene? Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
4 Total E ect When prices or income change, we move from one equilibrium bundle to another. The distance we move (in one dimension) is called the total e ect. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
5 Total E ect z A A Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
6 Total E ect z A B A B Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
7 Total E ect z A B A B Total Effect Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
8 Total E ect We can break the total e ect down into two components: the income e ect and the substitution e ect. Total E ect = Income E ect + Substitution E ect The income e ect measures the amount of the change in the total e ect that can be attributed to a change in income. Actual income doesn t have to change, though. A change in income could be represented as being able to a ord less of all goods due to a price increase. The substitution e ect measures the amount of the change in the total e ect that can be attributed to the change in relative prices. Even if we held income constant, if prices change, we would substitute away from a more epensive good to a cheaper good. Let s start with the income e ect. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
9 Income E ect When we vary the income level of a consumer, we do not eperience a substitution e ect. This is because the relative prices do not change. Recall that as income increases, the budget line shifts outward, and more of at least one of the goods will be consumed. If one of the goods is inferior, its consumption will actually decrease. We can connect the dots of all of the bundles that we consume to show how consumption changes as income changes. We call this a wealth epansion path. (Note: Perlo calls this the Income-consumption curve, but it s more commonly known as a wealth epansion path.) Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
10 Income E ect z A A Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
11 Income E ect z A B A B Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
12 Income E ect z A B C A B C Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
13 Income E ect z Wealth Epansion Path A B C A B C Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
14 Income E ect Notice that in our eample, the consumption of both goods ( and z) increase as income increases. This implies that both goods are normal, as opposed to inferior. We can attach a gure of the demand curves to the bottom of the indi erence curves to show that increasing income is causing the demand curve to shift to the right. How do we know that they are shifts? The prices are being held constant. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
15 Income E ect z A B Wealth Epansion Path C p D A D B D C A B C Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
16 Income E ect We can also attach another gure to the bottom of our indi erence curves to plot the changes in quantity as a function of the income. This will look just like our wealth epansion path. When it is plotted by itself, we call it an Engel curve. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
17 Income E ect z A B Wealth Epansion Path C Y Engel Curve A B C Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
18 Income E ect The direction that the wealth epansion path travels is etremely important. It will vary depending on if the good is normal or inferior. We can also have situations where goods start o as normal goods, but become inferior as the income of the people purchasing them increases. A good eample of this is red meat. When people are poor, they tend to purchase more meat as their income increases due to its abundance of protein and iron. At a certain point, however, they start buying less red meat with additional income and choose to buy healtheir options instead, like seafood. The wealth epansion path will help us determine when a good turns from normal to inferior. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
19 Income E ect z Inferior z Normal Normal z Normal Normal z Inferior Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
20 Income E ect z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
21 Income E ect z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
22 Income E ect z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
23 Income E ect z Wealth Epansion Path Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
24 Income E ect Can we actually calculate the wealth epansion path? We actually already did. Recall the eample we did yesterday when we derived the demand curve for good. Our result was = 3Y 4p When we turned this into a demand curve, we assumed that we knew what Y (and everything else) was, and just varied p. Now, we do the opposite. We assume that we know what p (and everything else) is and we just vary Y. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
25 Income E ect z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
26 Income E ect z Wealth Epansion Path Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
27 Eample Let s practice this a little bit. Consider a consumer with the following utility function Ū = 0.5 z 0.5 Derive the demand functions for goods and z. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
28 Eample Ū = 0.5 z 0.5 Before we can get our demand functions, we need to gure out our tangency points, which require the marginal rate of substitution and marginal rate of transformation. Starting with the marginal rate of substitution, we need the marginal utilities for and z. MU = z 0.5 MU z = z 0.5 Net, we can combine them to nd the marginal rate of substitution MRS = MU = z 0.5 MU z z 0.5 = z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
29 Eample Now, we need the marginal rate of transformation, which is just the negative price ratio MRT = p p z Note that we can just leave it like this, since I didn t give any values for prices or income. We don t need them! Net, we set the marginal rate of substitution and the marginal rate of transformation equal to one another. and rearranging, we have MRS = MRT z p = p z p = p z z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
30 Eample p = p z z What does this statement mean? It means that the total money we spend on good (p ) will be equal to the total money we spend on good z (p z z). This should make sense, because the eponents for and z in the utility function were the same. The consumer gains the same amount of utility from both goods. But are they substitutes? Let s nd out. We need one more equation to solve for our demand functions, which is our budget constraint, p + p z z = Y Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
31 Eample p = p z z p + p z z = Y I can just substitute the rst equation right into the second equation to get p z z + p z z = Y 2p z z = Y and solving this epression for z gives our demand function for z, z = Y 2p z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
32 Eample z = Y 2p z Last, but not least, I plug this epression back into my tangency point equation and solve for to get the demand function for, p = p z z Y p = p z 2p z = Y 2p and there we have it, demands for both goods and z! = Y 2p z = Y 2p z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
33 Eample = Y 2p z = Y 2p z Let s analyze these a bit. Are and z substitutes (like we wondered before)? No. Since the price of good z doesn t show up in good s demand function, they don t a ect one another. Thus, they are neither substitutes nor complements. Are goods and z normal? Yes. They both are. If Y goes up, both and z go up. Thus, if the consumer s income rises, they consume more of both goods, making them both normal. What way should we epect the wealth epansion path to go? Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
34 Eample = Y 2p z = Y 2p z Let s set p = 2 and p z = 4. Our demand functions become = Y 4 z = Y 8 Now, I can pick di erent values for Y and this will give corresponding values of and z. Y z Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
35 Eample z 2 4 Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
36 Eample z 2 4 Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
37 Eample z 2 4 Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
38 Eample As we can see, the wealth epansion path passes right through our equilibrium allocation. This will always happen. For every other value of income, the new budget line and utility curve will be tangent at eactly their corresponding point on the wealth epansion path. Also, the wealth epansion path moves to the top right of the gure, just like we would epect for two normal goods. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
39 Summary To summarize, if we hold all prices constant and just vary income, the wealth epansion path will include all of our possible equilibrium points for the constrained consumer choice problem. Also, if prices are held constant, the total e ect and the income e ect are the same thing. i.e., the substitution e ect equals 0. Net time, we ll add the substitution e ect in. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
40 Preview for Friday The Substitution E ect. We ll see what happens when relative price changes enter into the problem. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
41 Assignment 3-2 (1 of 1) 1. Return to the same utility function we analyzed in assignment 3-1. Ū = 0.2 z 0.8 a. Holding prices constant at p = 2 and p z = 4, pick three values for income and plot the optimal quantities of and z on a gure. Use these points to derive the wealth epansion path graphically. Eric Dunaway (WSU) EconS Lecture 13 September 23, / 41
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