Labor Supply 1 - Lecture Notes PDF

Labor Supply 1 Daeun Sung Texas A&M Jan 28, 2025 Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Today 1. Data and the Labor Force 2. Preference and Utility 3. Prac...

Labor Supply 1 Daeun Sung Texas A&M Jan 28, 2025 Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Current Population Survey (CPS) One of the oldest, largest, and most well-recognized surveys in the United States Primary source of monthly labor force statistics Website: https://www.census.gov/programs- surveys/cps.html We are going to use CPS to know basic information about the labor market Definitions Basic definition for individuals 16 and older and not institutionalized, for reference week Employed (E): work at least 1 paid hour or 15 non-paid hours Unemployed (U): temporary lay off or actively looking for work in the previous 4 weeks Population (P): all individuals in the relevant age range Labor Force (LF): LF = E + U Out of Labor Force (OLF): P = LF + OLF Institutionalized = going to school, so we are not counted Why do we count 15 non-paid hours? (working for family business or internship) Labor force categories Labor force, 2019 More Definitions And more… Labor Force Participation Rate = LF / P Employment Rate = E / P Unemployment Rate = U / LF More Definitions Some Limitation The official definition of U makes sense because some people choose not to work (retired, some parents, etc.) But it misses the “Hidden Unemployed”: an individual who has applied for jobs for 36 weeks, and then gives up looking (i.e., a “discouraged worker”) is OLF The official definition of U misses work intensity and work quality “Under employed” is sometimes used to described part-time workers who wish to work fulltime and workers who take a much-lower skilled job These simple definitions aren’t broken—they are just simple LFPR, 1950-2016 Older people are healthier and living longer (due to technology, medicine) & jobs have less manual labor – aren’t retiring as early Women’s LFPR, 1968-2016 The basic facts LFPR for men: Has always declined with age For 55+: strongly declined over the 1900s but recently rebounded For 25-54: remained relatively high over the 1900s, but has declined somewhat LFPR for women Has increased for all groups, but increased most strongly for married women Married LFPR has converged with singles More definitions We often quote these statistical concepts for narrower groups to help with interpretation LFPR for women 25-54 avoids schooling and retirement Definitions Extensive margin: whether one works at all Intensive margin: the number of hours one works Extensive vs. intensive margin Average weekly hours worked Over-time hours policy changed pre-WWII Hours worked increased during the war More facts LFPR and annual hours worked increases with education LFPR declines more with age than does annual hours LFPR differences by race tend to be bigger than annual hours differences Average weekly hours have declined strongly over time More women than men work part-time. More men who are high school dropouts work than women who are high school dropouts. Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Our basic model “Neoclassical static labor supply model” Neoclassical: We assume that workers are maximizing a utility function, valuing consumption and leisure Consumption is every purchased goods and services Leisure is a catch-all for not working—so more leisure is less working Very similar to the intermediate micro model where an individual is choosing to consume two goods Static: We consider a one-period model Our basic model The basic components Preferences over two goods, consumption and leisure, represented by a utility function A budget constraint The assumption that individuals choose the bundle that provides maximum utility, subject to the budget constraint Assumptions about Preferences Economists assume individuals are rational and able to optimize consumption decisions given scarce resources. 1. Completeness and rankability Individuals can compare bundles of goods and rank them 2. For most goods, more is better than less (“monotonicity”) Non-satiation If I prefer A to B and I prefer B to C, then I 3. Transitivity prefer A to C Imposes consistency on rankings 4. The more one has of a particular good, the less he is willing to give up of something else to get even more of that good Utility Utility: a function that returns the value of consuming a particular bundle Utility (U) is generated by consuming consumption goods (C) and leisure (L) based on some function f(.): U=f(C,L) For a particular f(.), we could compute utility (in utils) for a particular value of C and L Example Suppose U=(C/1000) x (L/100), C=$55,000, L=1200 hrs U = 55 x12 = 660 utils Indifference Curves Indifference curve: a curve that connects all bundles that deliver an identical value of utility Suppose U=(C/1000) x (L/100) One could find all values of C and L such that U=660 utils A utility function implies a collection or field of indifference curves Example: two indifferences curves from a utility function Properties of indifference curves We make assumptions about utility/preferences that have implications for what indifference curves must look like 1. Indifference curves are downward-sloping This follows from an assumption that consumers value both consumption and leisure (that consumption and leisure are both “goods”) Why? If we are to keep utility constant while taking away consumption, we must offer the individual more leisure 2. Indifference curves further from the origin (higher) represent higher levels of utility This follows in part from the same assumption that C and L are “goods”— more of both must lead to higher utility It also requires a “non-satiation” assumption—that more of a good is always better Properties of indifference curves 3. Indifference curves cannot cross Why? It would lead to a logical inconsistency The graph to the right suggests U(X)=U(Y), U(Y)=U(Z), and U(Z)>U(X), which cannot be simultaneously true (if utility follows “transitivity”) Properties of indifference curves 4. Indifference curves are convex to the origin This follows from a much different assumption, one about “diminishing marginal utility” Diminishing marginal utility is the assumption that each additional unit of consumption, all else equal, delivers less additional utility “Concave makes a cave” Concave Convex to origin to origin Differences in Preferences Steep curve = values leisure more Need MORE consumption to give up one unit of leisure. Workers with steeper indifference curves value their leisure relatively more than workers with shallower indifference curves. Differences in Preferences: Video Games Suppose Cameron greatly enjoys playing video games and greatly dislikes working. Which of the indifference curves above do you think reflect Cameron’s preferences? Why? Differences in Preferences: Great Resignation Suppose that many workers become greatly dissatisfied with their jobs, work- life balance, and managers. Which indifference curves do you think best reflect their preferences? Why? Differences in Preferences: Family Care Suppose that Leslie has two small children, and childcare in her area is extremely expensive. Which indifference curves do you think best reflect Leslie’s preferences? Why? Differences in Preferences: Workaholic Suppose that Erin greatly enjoys working everyday, but she does not enjoy having a lot of free time outside of work. Which indifference curves do you think best reflect Erin’s preferences? Why? Differences in Preferences: Work-Life Balance How does the trade-off between consumption and leisure change as the person “rolls down” the indifference curve? How does this relate to the assumption of convexity? Marginal utility Marginal utility is the additional utility that is obtained by consuming one additional good, holding the other good(s) constant In our problem, we have two goods, C and L, so there are two marginal utilities Marginal utility In terms of calculus: Marginal utility of consumer goods: MUc = ∂U(C,L) / ∂C Marginal utility of leisure: MUL = ∂U(C,L) / ∂L Assumptions/properties The marginal utilities must be positive: consuming more goods always delivers positive utility There must be diminishing marginal utility: the indifference curves are convex to the origin  Marginal rate of substitution (MRS) The indifference curve tells us how an individual is willing to trade between the goods Moving between X and Y, this person is willing to give up $100 in consumption for 25 hours of leisure when holding utility constant Going from 125 to 150 hours, the person is willing to give up less consumption compared to going from 100 to 125 MRS = tradeoff between two marginal utilities Marginal rate of substitution (MRS) The slope of the indifference curve tells us how a person is willing to trade between the two goods Slope: C MU L = L MU C We drop the negative sign when we look at MRS MU L MRS: MRS = MU C Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Practice 1 Let U(C,L) = f(C,L); suppose the following are true: U(75,20) = 2,500; U(50,30) = 2,500; U(35,40) = 2,500 Can you draw an indifference curve that includes these bundles of consumption and leisure? What about U(55,40) = 3,000? Practice 2 Let U(C,L) = f(C,L); Kurt’s utility function is as below U(C,L) = C x L What is his MRS? Practice 2 Let U(C,L) = f(C,L); Kurt’s utility function is as below U(C,L) = C x L What is his MRS? 𝑀𝑈𝐿 = C 𝑀𝑈𝑐 = L 𝑀𝑈𝐿 𝐶 MRS = | |=| | 𝑀𝑈𝐶 𝐿 Practice 3 Let U(C,L) = f(C,L); Paula’s utility function is as below U(C,L) = 2𝐶 3 𝐿 + 𝐶𝐿2 What is her MRS? Practice 3 Let U(C,L) = f(C,L); Paula’s utility function is as below U(C,L) = 2𝐶 3 𝐿 + 𝐶𝐿2 What is her MRS? 𝑀𝑈𝐿 = 2𝐶 3 + 2𝐶𝐿 𝑀𝑈𝑐 = 6𝐶 2 𝐿 + 𝐿2 𝑀𝑈𝐿 2𝐶 3 +2𝐶𝐿 MRS = | |=| 2 | 𝑀𝑈𝐶 6𝐶 𝐿+ 𝐿2 Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Budget constraint Second Component of “neoclassical static labor supply model” Since we assume that both C and L are always “goods”, then individuals would want to consume as much of both as possible. The budget constraint is what limits consumption Wage (w) is the hourly wage an individual can earn Hours (h) is the number of hours an individual works Non-labor income (V) is a person’s income that doesn’t depend on work A few comments Remember that we called this a “static” model. Think of a person living just one year, and choosing C and L for that year Implications: C will equal total income, and we can ignore assets/savings This simplification makes things much easier… Budget constraint Money budget constraint: C = w*h + V A person’s dollar value of expenditures (C) must equal the sum of their labor income (w*h) and non-labor income (V) Time budget constraint: T = h + L There is total number of hours available (T) to be divided between work (h) and leisure (L) Full budget constraint: C = w(T-L) + V = (w*T + V) – wL Or: C + w*L = w*T + V (w*T + V) is sometimes referred to as “full income”—the total amount an individual could earn if they spent all of their time working Individuals then choose to spend full income on purchasing two goods, C and L This makes clear that the price of leisure is the wage rate Budget line Budget line Endpoints L=0: C=wT + V L=T: C=V E is sometimes called the endowment point The slope: -w The financial trade-off between L and C: the wage Consumption opportunity set The budget line and all points below The consumer version of a PPF Non-Standard Budget Constraint What happens if prices are not constant? How does this change the shape of the budget constraint? Do you pay the same amount for each kilowatt hour on your electricity bill? If not, are your incentives changed because of a non-constant prices? Should we expect a constant take-home wage rate? Can you think of some scenarios where the take-home wage changes depending on an individual’s hours worked or income? Overtime pay over 40 hours A tax on wages for income over a certain $ amount. A subsidy on wages for income over or under a certain $ amount. Graphing a “Kinked” Budget Constraint Suppose that non- labor income is V, the take-home wage rate is w, and total weekly hours is T. Also, suppose that there is a 50% tax rate for all hours worked over 40 hours. Today 1. Data and the Labor Force 2. Preference and Utility 3. Practice Problems 4. Budget Constraint 5. Budget Constraint Practice Problems Practice 1 Can you write consumption (C) using wage (w), working hours (h), and non-labor income (V)? Can you write consumption (C) using wage (w), total hours (T), leisure hours (L), and non-labor income (V)? Can you write the maximum amount of consumption? Can you write the minimum amount of consumption? C = wh + V C = w(T-L) + V C = wT + V C=V Practice 2 Suppose that there are 110 hours of total time in the period. Jessie’s (take home) wage (w) is $10 per hour. For now, suppose Jessie receives no nonlabor income V. What is Jessie’s maximum amount of consumption? This occurs at what values of L? What is Jessie’s minimum amount of consumption? This occurs at what values of L? Can you use this information to graph Jessie’s budget constraint? Jessie’s maximum amount of consumption is $1100 (when L = 0). Jessie’s minimum amount of consumption is $0 (when L = 110). Practice 3 What is the budget line for consumption (C) and leisure (L) if a person faces a constant wage of $5 per hour, there are 168 hours in the week to work, and she receives non-labor income of $200 per week? Practice 3 What is the budget line for consumption (C) and leisure (L) if a person faces a constant wage of $5 per hour, there are 168 hours in the week to work, and she receives non-labor income of $200 per week? C = w(T-L) + v C = 5(168 – L) + 200 C = 840 – 5L + 200 C = 1040 – 5L (when L =< 40) Practice 4 What is the budget line for consumption (C) and leisure (L) if a person faces a wage of $5 per hour up to 40 hours and $10 per hour after 40 hours, there are 168 hours in the week to work, and she receives non-labor income of $200 per week? when L = 128, w*H = 5*40 = 200, C = 400 Let’s call w1 = 5, w2 = 10 Practice 4 What is the budget line for consumption (C) and leisure (L) if a person faces a wage of $5 per hour up to 40 hours and $10 per hour after 40 hours, there are 168 hours in the week to work, and she receives non-labor income of $200 per week? C = 40*w1 + w2((T – L) – 40) + V C = 200 + 10((168 - L) - 40) + 200 C = 200 + 1280 – 10L + 200 C = 1680 – 10L Announcements Reading Assignment due on Feb 3rd In the next class, we will continue the labor supply