class: center, middle, inverse, title-slide # The Worker’s Dilemma ## EC 350: Labor Economics ### <a href="https://kyleraze.com">Kyle Raze</a> ### Winter 2022 --- # The Worker's Dilemma **Q:** Why do we work? -- **A.sub[1]:** In pursuit of meaning? For enjoyment? To feel useful? - Some jobs provide more than compensation. - Other jobs? [Not so much](https://www.marketplace.org/shows/the-uncertain-hour/to-catch-a-chicken/). -- **A.sub[2]:** To make money for purchasing goods and services! - The bills aren't going to pay themselves! --- # The Worker's Dilemma **Q:** What do we give up by working? -- **A:** Time spent doing leisurely.super[.hi-pink[<span>&#8224;</span>]] activities! .footnote[.hi-pink[<span>&#8224;</span>] In economics, ***leisure*** .mono[=] *any activity that **doesn't involve working for money** or other remuneration*.] - Sitting on the couch - Going on vacation - Spending quality time with your friends and family -- - Exercising - Raising children - Studying - Eating - Sleeping - Cleaning your apartment --- # The Worker's Dilemma **Q:** Why must we make choices about spending our time and money? -- **A: Scarcity!** - **Time is scarce:** There are only 24 hours in a day, and even though [human lifespans are increasing](https://www.gapminder.org/fw/world-health-chart/), we still must grapple with our **finite** existence. - **Resources are scarce:** While [living standards are increasing](https://www.gapminder.org/fw/income-mountains/), there still **isn't enough** of the things we like to satisfy our unlimited desires. -- When resources are scarce, the decision **to do one thing** necessarily implies that **something else doesn't get done.** --- # Choices .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-1-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ An individual worker's choices are characterized by **observable quantities:** - Daily earnings, or total income - Daily hours worked .mono[-->] hours of leisure ] --- count: false # Choices .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-2-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ An individual worker's choices are characterized by **observable quantities:** - Daily earnings, or total income - Daily hours worked .mono[-->] hours of leisure Typically, these quantities are all we can see in the data. - To understand *how* workers make choices, **we need a theory!** ] --- # Labor-leisure model **Q:** How do workers make **labor supply** decisions? - What factors induce individuals to enter the labor market? - What factors influence *how much* individuals work once they are in the market? -- The **labor-leisure model**.super[.hi-pink[<span>&#8224;</span>]] examines how workers respond to incentives given information about their ***opportunities*** and their ***preferences***. - The model allows us to generate **testable predictions** about individual responses to changes in market conditions. .footnote[.super[.hi-pink[<span>&#8224;</span>]] Developed by [Gary Becker](https://en.wikipedia.org/wiki/Gary_Becker), an influential economist, in [A Theory of the Allocation of Time](https://academic.oup.com/ej/article-abstract/75/299/493/5250146), *The Economic Journal* (1965).] --- # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ From before, we saw that the worker selected the bundle (L .mono[=] 16, Y .mono[=] 30). - It must have been the case that the bundle was **feasible** for the worker. ] --- count: false # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-4-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ From before, we saw that the worker selected the bundle (L .mono[=] 16, Y .mono[=] 30). - It must have been the case that the bundle was **feasible** for the worker. ### **Opportunity set** > The set of all possible (L, Y) bundles available to a worker. ] --- # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-5-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** What determines a worker's opportunity set? ] --- count: false # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-6-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** What determines a worker's opportunity set? **A:** The number of hours in a day and the .green[budget constraint], given by `$$\begin{align} \color{#007935}{Y} &\color{#007935}{= wH + v} \\ &\color{#007935}{= w(24 - L) + v} \end{align}$$` - `\(H\)` .mono[=] number of hours worked - `\(w\)` .mono[=] best hourly wage available to the worker - `\(v\)` .mono[=] non-labor income ] --- # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-7-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** What determines a worker's opportunity set? **A:** The number of hours in a day and the .green[budget constraint], given by `$$\begin{align} \color{#007935}{Y} &\color{#007935}{= wH + v} \\ &\color{#007935}{= w(24 - L) + v} \end{align}$$` **Example** - `\(w\)` .mono[=] 3 - `\(v\)` .mono[=] 0 ] --- count: false # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-8-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** What determines a worker's opportunity set? **A:** The number of hours in a day and the .green[budget constraint], given by `$$\begin{align} \color{#007935}{Y} &\color{#007935}{= wH + v} \\ &\color{#007935}{= w(24 - L) + v} \end{align}$$` **Example** - `\(w\)` .mono[=] 6 - `\(v\)` .mono[=] 0 ] --- count: false # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-9-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** What determines a worker's opportunity set? **A:** The number of hours in a day and the .green[budget constraint], given by `$$\begin{align} \color{#007935}{Y} &\color{#007935}{= wH + v} \\ &\color{#007935}{= w(24 - L) + v} \end{align}$$` **Example** - `\(w\)` .mono[=] 6 - `\(v\)` .mono[=] 15 ] --- # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-10-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will the worker respond if her previous choice is no longer feasible? ] --- count: false # Opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-11-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will the worker respond if her previous choice is no longer feasible? **A:** 🤷 - To predict a worker's response to a changes in her opportunity set, we also must consider her **preferences** over available alternatives. ] --- # Preferences **Q:** Can we measure preferences? -- - **A:** Not typically. -- Our inability to measure preferences requires us to make assumptions. - However defined, **preferences do not change** during the course of the analysis. -- **Four behavioral postulates** give us the ability to model labor supply: 1. People have preferences 2. People prefer more over less 3. People are willing to substitute 4. Marginal utility is decreasing --- # Preferences ## **Utility function** We can describe a worker's preferences over leisure and consumption using a utility function: `$$U = f(L, Y)$$` - `\(U\)` represents the worker's **well-being** or life satisfaction (higher is better). - `\(L\)` represents hours of leisure, a "good." - `\(Y\)` represents total (real) income, which we assume will be spent on goods and services. - The functional form of `\(f(\cdot)\)` satisfies the four behavioral postulates. -- **Q:** The worker only cares about leisure and consumption? Really? -- <br> **A:** There are many things we could include in the utility function, but to make testable predictions, **we need to abstract away from unnecessary details**. > A theory that explains everything, explains nothing. &nbsp;&nbsp; &mdash; [Karl Popper](https://en.wikipedia.org/wiki/Karl_Popper) --- # Preferences .pull-left[ <div id="htmlwidget-7c11065baa5a37decf9e" style="width:100%;height:504px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-7c11065baa5a37decf9e">{"x":{"visdat":{"1c3422f06474":["function () 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] .pull-right[ **Q:** How does this **utility function** incorporate the four behavioral postulates? 1. People have preferences? 2. People prefer more over less? 3. People are willing to substitute? 4. Marginal utility is decreasing? ] --- # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-13-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### .hi-pink[Indifference curves] Each **indifference** curve describes the set of `\((L, Y)\)`-bundles that yield the **same level of utility**. ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-14-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### .hi-pink[Indifference curves] Each **indifference** curve describes the set of `\((L, Y)\)`-bundles that yield the **same level of utility**. - The worker is indifferent between bundle **A** and bundle **B**. ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-15-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### .hi-pink[Indifference curves] Each **indifference** curve describes the set of `\((L, Y)\)`-bundles that yield the **same level of utility**. - The worker is indifferent between bundle **A** and bundle **B**. - The worker prefers bundle **C** over **A** or **B**. ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-16-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### .hi-pink[Indifference curves] Each **indifference** curve describes the set of `\((L, Y)\)`-bundles that yield the **same level of utility**. - The worker is indifferent between bundle **A** and bundle **B**. - The worker prefers bundle **C** over **A** or **B**. The **indifference map** informs us about ***what is desirable*** from the perspective of the worker. ] --- # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-17-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** The slope of an indifference curve describes the **marginal rate of substitution of leisure for income:** `$$\text{MRS}_{L, Y} = - \dfrac{\text{MU}_L}{\text{MU}_Y}$$` - `\(\text{MU}_L\)` .mono[=] marginal utility of leisure - `\(\text{MU}_Y\)` .mono[=] marginal utility of income **Interpretation:** The amount of income a worker would *willingly* sacrifice for an additional hour of leisure. ] --- # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-18-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** **Q:** How do we interpret `\(\text{MRS}_{L, Y}\)` .mono[=] -16? ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-19-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** **Q:** How do we interpret `\(\text{MRS}_{L, Y}\)` .mono[=] -8.16? ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-20-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** **Q:** How do we interpret `\(\text{MRS}_{L, Y}\)` .mono[=] -4.94? ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-21-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** **Q:** How do we interpret `\(\text{MRS}_{L, Y}\)` .mono[=] -3.31? ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-22-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Marginal rate of substitution** **Q:** How do we interpret `\(\text{MRS}_{L, Y}\)` .mono[=] -1.78? ] --- count: false # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-23-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Diminishing marginal rate of substitution** The worker becomes less willing to sacrifice income for leisure as income decreases. - As `\(Y\)` decreases relative to `\(L\)`, `\(|\text{MRS}_{L, Y}|\)` decreases. **Why?** Indifference curves are **convex**. - An average of two extreme bundles is preferable to either of the extreme bundles. ] --- # Preferences .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-24-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### .hi-pink[Indifference curve properties] 1. Indifference curves have negative slopes 2. Higher indifference curves .mono[-->] higher utility 3. Indifference curves are convex ] --- # Preferences ## **Objective function** We assume that the worker seeks maximize her utility given the set of available opportunities: `$$\max\limits_{L,Y} U(L,Y) \space \text{ s.t. } \space Y = w (24 - L) + v$$` - The worker chooses a feasible bundle `\((L^*, Y^*)\)` that yields the highest utility. - In other words, the worker solves a **constrained optimization** problem..super[.hi-pink[<span>&#8224;</span>]] .footnote[.super[.hi-pink[<span>&#8224;</span>]] Yet another reason why calculus is useful.] -- .hi-pink[Maximizing] your utility .mono[-->] "living your .hi-pink[best] life" --- # Preferences .mono[+] opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-25-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? ] --- count: false # Preferences .mono[+] opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-26-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** No! - **Why?** ] --- count: false # Preferences .mono[+] opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-27-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** No! - **Why?** There are other feasible bundles that yield higher utility! - In this case, the worker could&mdash;without incurring additional cost&mdash;increase leisure, income, or both. ] --- # Preferences .mono[+] opportunities .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-28-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ ### **Opportunity cost** In fact, the worker will **always choose** a bundle somewhere **along the budget constraint**. For this reason, we can interpret the slope of the budget constraint as the **opportunity cost**.super[.hi-pink[<span>&#8224;</span>]] of an additional hour of leisure. - For each additional hour of leisure, you must sacrifice `\(w\)` dollars. .footnote[.super[.hi-pink[<span>&#8224;</span>]] *Opportunity cost* .mono[=] The forgone value of *your* next-best alternative.] ] --- # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-29-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? ] --- count: false # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-30-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** No. At the current bundle, - **MRS** .mono[=] -25 - **Opportunity cost** .mono[=] -5 The cost of an additional hour of leisure **is less than** the worker's willingness to pay for additional hour of leisure! ] --- # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-31-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? ] --- count: false # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-32-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** No. At the current bundle, - **MRS** .mono[=] -10 - **Opportunity cost** .mono[=] -5 The cost of an additional hour of leisure **is less than** the worker's willingness to pay for additional hour of leisure! ] --- # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-33-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? ] --- count: false # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-34-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** No. At the current bundle, - **MRS** .mono[=] -2.5 - **Opportunity cost** .mono[=] -5 The cost of an additional hour of leisure **is greater than** the worker's willingness to pay for additional hour of leisure! ] --- # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-35-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? ] --- count: false # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-36-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** Has this worker maximized her utility? **A:** Yes! At the current bundle, - **MRS** .mono[=] -5 - **Opportunity cost** .mono[=] -5 The cost of an additional hour of leisure **equals** the worker's willingness to pay for additional hour of leisure! ] --- # Optimization .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-37-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ The worker chooses the optimal bundle `\((L^*, Y^*)\)` where `$$\text{MRS}_{L, Y} = - w$$` - That is, where the indifference curve is **tangent** to the budget constraint. ] --- # Optimization ## **Intuition?** At the optimal bundle, `$$\begin{align} \dfrac{\text{MU}_L}{\text{MU}_Y} &= w \\ \text{MU}_Y &= \dfrac{\text{MU}_L}{w} \end{align}$$` -- - `\(\text{MU}_Y\)` .mono[=] additional utility from spending one more dollar on consumption - `\(\text{MU}_L\)` .mono[=] additional utility from one more hour of leisure - `\(\dfrac{\text{MU}_L}{w}\)` .mono[=] additional utility from spending one more dollar on leisure -- **In words?** The worker maximizes utility when the last dollar spent on leisure buys the same amount of utility as the last dollar spent on consumption. --- # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-38-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in non-labor income? ] --- count: false # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-39-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in non-labor income? ] --- count: false # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-40-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in non-labor income? **A:** The worker will work fewer hours. - We will always define preferences such that leisure is a **normal good**..super[.hi-pink[<span>&#8224;</span>]] .footnote[.super[.hi-pink[<span>&#8224;</span>]] *Normal good* .mono[=] A good for which consumption increases as wealth increases.] ] --- # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-41-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in the hourly wage? ] --- count: false # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-42-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in the hourly wage? ] --- count: false # Worker responses .pull-left[ <img src="06-Workers_files/figure-html/unnamed-chunk-43-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ **Q:** How will this worker respond to an increase in the hourly wage? **A:** In this case, the worker will work additional hours. - The direction of the response depends on wealth and substitution effects. (More on this later.) ] --- # Comparing workers .pull-left[ .center[.hi-pink[Money lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-44-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ .center[.hi-purple[Leisure lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-45-1.svg" style="display: block; margin: auto;" /> ] --- # Comparing workers .pull-left[ .center[.hi-pink[Money lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-46-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ .center[.hi-purple[Leisure lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-47-1.svg" style="display: block; margin: auto;" /> ] --- # Comparing workers .pull-left[ .center[.hi-pink[Money lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-48-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ .center[.hi-purple[Leisure lover]] <img src="06-Workers_files/figure-html/unnamed-chunk-49-1.svg" style="display: block; margin: auto;" /> ] --- # Implications for policy? Even in a truly equal-opportunity world.super[.hi-pink[<span>&#8224;</span>]], **differences in preferences will lead to unequal outcomes** (*e.g.,* earnings). .footnote[.super[.hi-pink[<span>&#8224;</span>]] Not this one!] **Q:** Is this bad? -- **A:** This is fundamentally a normative question. But **a policy that forces people** with different preferences **to make the same choices** without compensation **will necessarily make someone worse off** without helping anyone else. - No normative claim here! This is a positive statement (someone *will* end up on a lower indifference curve). --- # Housekeeping **Assigned reading for Wednesday:** [Snapping back: Food stamp bans and criminal recidivism](https://www.aeaweb.org/articles?id=10.1257/pol.20170490) by Cody Tuttle (2019). - Reading Quiz 3 due by Wednesday, January 26th at 12pm (noon). - Check out the "Learning from Observational Data" lecture before you read the paper! - Pay special attention to the "regression discontinuity" section (slide 17, starts at roughly 44:30 in the video). **Assigned reading for Monday:** [Effective policy for reducing poverty and inequality? The Earned Income Tax Credit and the distribution of income](http://jhr.uwpress.org/content/early/2017/07/05/jhr.53.4.1115.7494R1.abstract) by Hilary Hoynes and Ankur Patel (2018). - Reading Quiz 4 will open after class on Wednesday and will be due by Monday, January 31st at 12pm (noon). **Problem Set 1** due by Friday, January 28th at 11:59pm. <!-- --- --> <!-- # Understanding worker responses --> <!-- [illustrate pure wealth effect; leisure is a normal good, etc.] --> <!-- --- --> <!-- # Understanding worker responses --> <!-- [Q: what happens when wages increase? A: worker becomes "richer" but also there's a change in incentives; we refer to the change in incentives as a substitution effect] --> <!-- --- --> <!-- # Understanding worker responses --> <!-- [derive substitution effect] --> <!-- --- --> <!-- # Deriving the labor supply curve --> <!-- [derive the neoclassical labor supply curve (u-max on the left, supply curve on the right)...illustrate the reservation wage and where income effect starts to dominate] -->