Illustration of Substitution Effect of Increasing Consumption TaxNotes 4: Labor Markets and UnemploymentI. Labor Supply and Labor DemandA) Labor Supply BackgroundRecall from Topic 2, we discussed the difference between the income and substitutioneffect. The income effect says that as people become richer, they want to work less.The substitution effect says that as the price of a good goes up today (i.e., leisure), thenyou want less of that good and more of other goods (in this case, less leisure and moreconsumption - how do you get more consumption? - work more to earn more).In micro, you probably learned models with two goods. I am going to go through a quickexample of two goods and then we will take it to the macro level. Suppose you onlywant to consume apples and bananas. Suppose further that you like consuming thesegoods. Think about your own consumption decision. If the price of apples increases -you are going to switch towards bananas. Remember from micro, we are going toconsume until the marginal utility of (apples)/ price of (apples) = marginal utility of(bananas)/ price of (bananas). Or,MU(apples)/P(apples) = MU(bananas)/P(bananas)If the price of apples increases, you need the marginal utility of apples to increase inorder for this equality hold. How do you get the marginal utility of apples to increase?You consume LESS apples (this is the law of diminishing marginal utility - the more youconsume of a good, the LESS extra utility you get - think about it, the 10th hamburger isnot as satisfying as the 1st.). This is the substitution effect. As the price of applesincrease, you are going to substitute away from apples towards bananas. But, as the price of apples increase, you spend more for the apples you buy. That means,in some sense - you are relatively poorer. You could not have bought the same bundle ofapples and bananas as you did before the price changed at the same cost after the pricechange. Given that you are poorer (due to the price change), you will buy less ofeverything you like (apples and bananas). This is the income effect. As the price ofapples increase, you will decrease your consumption of BOTH apples and bananas. Notice, as the price of apples increase, you will definitely decrease your consumption ofapples (income and substitution effect both say that you will consume less apples).However, your change in your consumption in bananas in response to an increase in theprice of apples is ambiguous. This is exactly the same type of analysis we will do in our class. 1B) Formalizing Labor SupplyIn macro, we assume households only care about 2 aggregate goods: consumption andleisure. Consumption is everything we buy (apples, bananas, golf lessons, cars, etc.).Leisure is how much we value not working. All else equal, people prefer to receivemoney without allocating time to work. As discussed in class, which of the followingjobs would you prefer?Job 1: Earn $250,000/ year and be expected to work 60 hours/week.Job 2: Earn $250,000/ year and be expected to work 30 hours/week.In both cases, the amount of consumption that could be purchased is the same (C =$250,000 (in a static model with no saving)). But, most people would prefer job 2 to job1. The reason is that people receive negative utility from the act of working itself. Or,the way we write it, people get positive utility from leisure time (i.e., the time they do notallocate to work). In other words, people will prefer hanging out with friends, sleeping,doing nothing, watching TV, etc. compared to going to work. Not all people are like this.Some people like working more than playing tennis or hanging out with friends. Onaverage, however, most people strictly prefer job 2 (above) to job 1 (above). Torepresent this in our models, we assume that people get direct utility from “leisure”.Some Assumptions:Individuals in the economy maximize the following utility function (over consumptionand leisure):U (C, L)The only assumption on the model that we will make is that marginal utility isdiminishing in consumption (individually) and leisure (individually). This implies thatthe marginal utility of consumption (leisure) decreases as consumption (leisure)increases. For simplicity throughout the remaining analysis, we will make three additionalassumptions:1. We will only consider a static model. This means that households only have aone-period planning horizon. In the next class (on consumption), we will relaxthis assumption. For our labor supply discussion, it adds little. 2. Consumption and Leisure are independent of each other such that the marginalutility of consumption (leisure) only depends on consumption (leisure). 3. There are only two things you can do with your time: either work (where N is the timespent working) or take leisure (where L is the time spent in leisure). I normalize the time2endowment to 1 such that N = 1 – L (by definition)). However, the normalization of thetime endowment does not matter. You could make that 24 (as in hours per day) or in 168(as in hours per week). The key assumption is that N and L are negatively related with acoefficient of 1 (a one hour increase in N implies – by definition – a one hour decline inL). Given this, we can express the optimization according to the following rules. To simplifyour analysis later on, I am going to directly embed consumption taxes (tc) and laborincome taxes (tn) into our analysis at this stage.Equation 1: Substitution Effect(1 ) (1 )CLc nMUMUP t W t=+ -Where MUC is the marginal utility of consumption, MUL is the marginal utility of leisure,P is the price of consumer goods in the economy (i.e., the CPI), W is the nominal wage, tcis the marginal tax rate on consumption (i.e., sales tax), and tn is the marginal tax rate onlabor income (i.e., the income tax). The price of consumption is the cost of consumption(P) plus any taxes someone pays on that consumption. The price of leisure is the wagesomeone earns from working less any taxes they pay on that labor income.The one interesting component of the above discussion is that the after tax wage is theprice of leisure. Why is that the case? In order for me to take one more hour of leisure, Ihave to give up an hour of work. The cost of giving up an hour of work is the