ECONOMIC THEORY 1A WEEK 3

Scarcity, Work, and Choice

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Outline

This lecture covers Chapter 3 of “The Economy” textbook. In this chapter, we will use economic models to:

1. Investigate decision making under scarcity: How do we meet our objectives given our limited means?
2. Model three different contexts in which different people decide how long to spend working, when facing a trade-off: A student, a farmer, and a wage earner.
3. Provide an explanation for why working hours have changed over time: Why does it differ between countries?

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Remember to use the Glossary section on www.core-econ.org

• https://core-econ.org/the-economy/book/text/50-02-glossary.html#glossary

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scarcity

• A [scarce good is a] good that is valued, and for which there is an opportunity cost of acquiring more.

opportunity cost

• When taking an action implies forgoing the next best alternative action. The cost of what you could not do because you did X.

economic cost

• The out-of-pocket cost of an action, plus the opportunity cost.

EXAMPLE OF A SOCCER FAN

• If you earn R50 a day and you have been offered a ticket to watch a soccer match for R40. As soccer fan you would value the experience at R100.
• Economic cost would be the out-of-pocket cost R40 plus the opportunity cost of not working R50 = R90
• Your enjoyment is valued at R100
• An economic model would predict that you would do it as your benefit > cost:
• enjoyment benefit (R100) > economic cost ( R90)
• Net benefit (economic rent) (R10)

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Introduction

• Decision making under scarcity is a common problem because we usually have limited means available to meet our objectives.
• Economists model these situations, first by defining all of the feasible actions, then evaluating which of these actions is best, given the objectives.
• A model of decision making under scarcity can be applied to the question of how much time to spend working (or studying) when facing a trade-off between more free time and more income (a higher grade).
• Trade-off – if more of x means less of y
• e.g if you want to get higher marks (x) you have to take less free time (y)

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Labour and Production�The production function, preferences, and the feasible set

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A note on ceteris paribus

• In economics, you will often see the Latin phrase “ceteris paribus.”
• From the glossary:
• The literal meaning of the expression is ‘other things equal’. In an economic model it means an analysis ‘holds other things constant.’
• Economists often simplify analysis by setting aside things that are thought to be of less importance to the question of interest.

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In building our models in this chapter, we will make many simplifying assumptions which help us “see more by looking at less.”

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How many hours to spend studying?

• As a student, you make a choice every day: how many hours to spend studying. 
• Many factors may influence your choice: how much you enjoy your work, how difficult you find it, how much work your friends do, and so on.
• Part of the motivation to devote time to studying comes from your belief that the more time you spend studying, the higher the grade you will be able to obtain at the end of the course. 
• We will construct a simple model of a student’s choice of how many hours to work, based on the assumption that the more time spent working, the better the final grade will be, ceteris paribus.
• The first building block of this model is called the production function.

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The Production Function

• Recall from Unit 2 that a production function is a graphical or mathematical expression that gives the maximum output for a given amount or combination of input(s).

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• A student’s production function translates the number of hours per day spent studying (her input of labour) into a percentage grade (her output).

Why is the production function shaped like that?

• The function is upward sloping (increasing) because of our assumption that the student can achieve a higher grade by studying more, ceteris paribus.
• In stating ceteris paribus, we are saying that the only thing that changes is the number of hours spent studying (the studying conditions, materials, method and so on all remain the same).
• The function is curved, starting with a steep slope that becomes flatter, because of diminishing returns (to studying). That is, the production function has a diminishing marginal product.

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marginal product

The additional amount of output that is produced if a particular input is increased by one unit, while holding all other inputs constant.

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Diminishing Marginal Product

• The student’s marginal product is the increase in her grade (output) from increasing her study time (input) by one hour.

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• Notice that the increase in final grade from studying 4 hours to studying 5 hours is 7, while the increase in final grade from studying 10 hours to studying 11 hours is only 3.
• The additional benefit of studying one more hour has diminished!

• A production function with this shape is described as concave.

Marginal Product and Average Product

• The marginal product is the slope of the line tangent to the production function.
• This will be the exact slope of the production function at a given number of study hours.
• At 4 hours of study, the marginal product is just above 7.

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• The average product is calculated by dividing total output (final grade) by a particular input (number of study hours).
• This gives the average number of percentage points per hour of study.
• At 4 hours of study, the average product is 12.5 ( = 50/4 ).
• At 10 hours of study, the average product is 8.1 (=81/10)

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• A diminishing marginal product implies that the average product is also diminishing.

So how many hours will the student study for?

• On its own, a production function cannot tell us what decision the student will make. Production function tells us about the objective relationship between study time and marks.
• The decision depends on the student’s subjective preferences.
• If she only cared about grades, she should study for 15 hours a day (and get the maximum possible mark of 90%). But the student also cares about her free time…
• So she faces a trade-off: how many percentage points is she willing to give up in order to have more free time to do things other than study?
• We now introduce the second building block of the model, which is called an indifference curve.

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Building an Indifference Curve

• An  indifference curve is a curve that connects the subjective combina­tions of goods that provide an individual with equal levels of utility or “satisfaction.”

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• In this case, the student wants a combination of a final grade and free time.
• The student is indifferent between points along the same indifference curve.
• NOTE: Y Axis is now HOURS OF FREE TIME, NOT STUDY HOURS)
• At A student has less free time (15 Hours, studies for 9 hours) and gets 84%
• At D student has more free time (20 hours, studies for 4 hours) and gets 50%
• Student is indifferent (equally happy) with A, E, F, G, H and D

Properties of Indifference Curves

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• Indifference curves slope downward due to trade-offs.
• Along a specific indifference curve more of one good must have less of the other good. You can’t have more free time and higher marks. Along an indifference curve you can be equally happy with high marks and less free time or 50% and lots of free time.
• Higher indifference curves correspond to higher utility levels.
• As indifference curves shift up and to the right, further away from the origin, this allows combinations with more of both high marks and free time. The student will always prefer to be on the highest indifference curve possible.
• Indifference curves are usually smooth.
• Small changes in the amounts of goods don’t cause big jumps in utility.
• Indifference curves do not cross for a particular person.
• Why? Since there cannot be a point an a higher utility curve that gives the same utility as a point on a lower utility curve
• As you move to the right along an indifference curve, it becomes flatter.

The Marginal Rate of Substitution (MRS)

• The slope of the indifference curve is called the Marginal Rate of Substitution (MRS). The MRS measures the trade-off that a person is willing to make between two goods, at a given point on the indifference curve.
• The MRS changes as we move along the curve:

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• At A, the student has an 84% grade, and 15 hours of free time. To gain one more hour of free time, the student is willing to sacrifice 9 percentage points, taking her to E.
• At H, the student has a 54% grade, and 19 hours of free time. To gain one more hour of free time, the student is only willing to sacrifice 4 percentage points, taking her to D (50%).

• Compared to when she is at AE, when the student is at HD she has low marks and relatively more free time, so she is willing to give up fewer marks to gain more free time.

The student’s dilemma…

• We can see that there are opportunity costs
• the cost of more free time is a lower grade
• the cost of higher marks is less free time
• So how does the student pick the best combination of final grade and free time that she can get – the one that most satisfies the student by giving her the highest possible utility?
• To answer this question, we need to adapt the production function into a model known as the feasible frontier.
• And we need to combine the objective feasible frontier with the student’s subjective indifference curve to model how much free time and how many marks she ultimately chooses in order to maximize her utility (satisfaction)

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The Feasible Frontier

• The feasible frontier is the curve made of points that give the maximum feasible (possible) final grade that the student can achieve, given how many hours of free time she has.

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• This is the mirror image of the production function we used earlier to determine the maximum possible grade the student could get, given the number of hours for which she studied.

The Feasible Set

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• The feasible set is the area under the feasible frontier that shows all of the feasible combinations of free time and final grade.

• It is not possible to reach a point outside of the feasible frontier.
• Any combination of free time and final grade that is on or inside the frontier is feasible.
• Inside the frontier the student could get a higher grade with the same amount of work or get the same grade with less work (more free time). (improve study methods at 14 hours free time to lift grade from 60% to 80%)
• Inside frontier increase y without decreasing x (no trade off between x and y).
• On frontier x up if y down. (there is a trade off between x and y)

Putting the Feasible Frontier and Indifference Curves together

• Now that we have indifferences curves and a feasible frontier that are on the same axes (free time and final grade), we can put the two curves together

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We can then find a point where the trade-off the student is willing to make (according to the slope of her subjective indifference curve) matches with a trade-off the student has to make (according to the slope of her objective feasible frontier).

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• Remember that the slope of the indifference curve is called the Marginal Rate of Substitution (MRS).
• The slope of the feasible frontier is called the Marginal Rate of Transformation (MRT).
• The MRT measures the quantity of one good that must be sacrificed to acquire one additional unit of another good.
• In this case, it is the rate at which the student can transform (or convert) reduced free time (increased study time) into final grade points.

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The MRS and the MRT

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• The MRS is the slope of the indifference curve. It measures the trade-off that the student is willing to make between final grade and free time.
• The MRT is the slope of the feasible frontier. It measures the trade-off that the student is constrained to make between free time and percentage points because it is not possible to go beyond the feasible frontier.

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• The student achieves the highest possible utility where the two trade-offs just balance.

• Her optimal combination of grade and free time is at the point where the MRT = MRS.

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• At this point, the indifference curve and the feasible frontier are tangential to each other.

Why is the optimal outcome at MRS = MRT?

• At B and D MRS > MRT
• The student’s subjective preference to increase free time even at the relatively high cost of lost marks is indicated by STEEP SLOPE (high MRS at B compared to E) (steeper slope = higher cost)
• The student’s objective ability to increased free time at a relatively low cost in terms of lost marks is indicated by LESS STEEP SLOPE (low MRT at B compared to E) (less steep slope = lower cost)
• Therefore, the student can indeed increase his or her free time without objectively having to sacrifice as many marks as he or she’s is subjectively prepared to sacrifice (as indicated by MRS > MRT)
• At B and D the opportunity cost of free time in the form of lost marks (MRT) is lower than the cost that the student is prepared to pay for free time in the form of lost marks (MRS) (MRT < MRS)
• Therefore, what happens at B and D?
• The student will continue demanding more free time and lower marks (moving from B to D to E) and each time will be gaining more utility as he or she will be on a higher indifference curve

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Why is the optimal outcome at MRS = MRT?

• At A MRT > MRS
• At A the opportunity cost of free time in the form of lost marks (MRT) is higher than the cost that the student is prepared to pay for free time in the form of lost marks (MRS)
• Therefore, what happens at A?
• The student will continue prefer less free time and higher marks (moving from A to E) and each time will be gaining more utility as he or she will be on a higher indifference curve

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Why is the optimal outcome at MRS = MRT?

• At E MRS = MRT
• When the students gets to E then MRS=MRT
• This is optimal for the student as it is on the highest indifference curve that intersects with the feasible frontier indicating the student’s highest feasible utility
• Model tells us that the optimal outcome is where MRS = MRT
• Student will study for five hours (19 hours free time) and will achieve 57%
• At E the opportunity cost of lost marks for increased free time (MRT) exactly matches the price that the student prefers to pay in the form of lost marks for increased free time (MRS)

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Hours of Work and Economic Growth�Technological Change

Another Constrained Choice Problem

• So far, we have considered how a student decides between studying and free time. This is called a constrained choice problem because the student had to make a choice between free time and a final grade, given her constrained (limited) time and productive capacity.
• We now apply our model to a self-sufficient farmer who chooses how many hours to work.
• We assume that the farmer produces grain to eat and does not sell it to anyone else. This is the only food the farmer has, so if he does not produce enough grain, he will starve.
• Like the student, the farmer also values free time. That is, he gets utility from both free time and consuming grain.
• There is an opportunity cost associated with both goods: having more free time means producing less grain, and producing more grain takes hours of labour that could otherwise be spent on free time.

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The Farmer’s Production Function

• This is the farmer’s initial production function which shows us that he can produce 64 units of grain if he works for 12 hours a day (point B).
• But what happens to this function if there is a technological improvement such as the invention of better farming equipment or seeds with a higher yield?

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Technological Change and the Production Function

• An improvement in technology means that more grain is produced for a given number of working hours. The production function shifts upward, from PF to PF_new.
• Now if the farmer works 12 hours per day, she can produce 74 units of grain (point C).
• Alternatively, by working 8 hours a day she can produce 64 units of grain (point D), which previously took 12 hours.

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Technological Change and the Feasible Frontier

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• Technological progress expands the feasible set: it gives the farmer a wider choice of combinations of grain and free time.
• The feasible frontier shifts upward, from FF to FF_new.

Optimal Choice before and after Technological Change

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• Technological progress raises the farmer’s standard of living: it enables him to achieve a higher utility than was previously possible.
• Note that, although the change definitely makes it feasible to both consume more grain and have more free time, whether the farmer will choose to have more of both depends on his preferences, and his willingness to substitute one good for the other.

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The farmer can move from point A on IC₃ to point E on IC₄, a higher indifference curve.

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But E is only one possible outcome, it will depend on the slope of the IC Curve and the famers preferences between free time and grain.

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Preferences are subjective

• We have seen that technological change has a number of effects on the farmer’s decision problem.
• It makes the production function steeper which increases the farmer’s marginal product of labour and makes the opportunity cost of free time higher.
• This could give the farmer a greater incentive to work, so he may decide to work more and have less free time. (SUBSTITUTION EFFECT)
• However, this change also means that the farmer can produce more grain in the same amount of time than he could before, so he may rather want to work less and have more free time. (INCOME EFFECT)
• These two effects of technological progress work in opposite directions.
• Let’s analyse income and substitution effects in more detail by looking at the choices of a wage earner deciding how many hours to work and how much of their income to spend each day, based on their hourly wage.

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The Budget Constraint

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Drawing the budget constraint

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The slope of the budget constraint corresponds to the wage: for each additional hour of free time (t), consumption must decrease by R150.

MRT – rate of transformation from free time into consumption.

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The area under the budget constraint is your feasible set (just like the farmer’s feasible set).

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So, the budget constraint here is just like the farmer’s feasible frontier!

The Optimal Choice

• Remember that the slope of the feasible frontier is called the marginal rate of transformation (MRT), and that it represents the opportunity cost of an hour of free time.
• The feasible frontier in this case is a straight line because the rate at which the wage earner can transform free time into consumption is equal to the magnitude of their hourly wage (R150) which is constant. (No diminishing returns – wage rate constant as free time is reduced)

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The wage earner’s preferred combination of consumption and free time will be where their indifference curve is tangential to their budget constraint:

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MRS = MRT = w

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At this point, their MRS —the rate at which they are willing to swap consumption for time — is equal to the wage.

Changes to the budget constraint: A Parallel Shift (Income effect)

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For each amount of free time, total income (earnings plus the birthday gift) is R500 higher than before. So the budget constraint is shifted upwards by R500 — the feasible set has expanded.

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This means that the new optimal choice is at point B on higher indifference curve, IC₃.

Changes to the budget constraint: A Swivel (Substitution effect)

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Now, for each hour of free time given up, the wage earner’s consumption can rise by R195 rather than R150. So the budget constraint swivels upwards along the y axis — the feasible set has expanded.

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This means that the new optimal choice is at point C on higher indifference curve, IC₄.

Different preferences yield different outcomes

Birthday Gift 🡪 Shift Wage Rise 🡪 Swivel

Work fewer hours Work more hours

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• Compare the outcomes in the two scenarios:
• With an increase in unearned income (the birthday gift), the wage earner decides work fewer hours (INCOME EFFECT)
• while the wage rise leads them to increase their working hours. (SUBSTITUTION EFFECT)
• These are only examples of outcomes in each scenario; an individual’s subjective preferences determine the final outcome (depending on slope of IC)

The Income and Substitution Effects if wages rise

So the rising wage has two THEORETICAL EFFECTS on the choice of free time:

1. The income effect (incentive to increase free time and work less as income rises)
2. The substitution effect (incentive to reduce free time and work more as opportunity cost of not working rises)

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The EMPIRICAL RESULT of a rising wage depends on whether the income effect or substitution effect is larger.

If income effect > substitution effect – free time increases (WORK LESS)

If substitution effect > income effect – free time falls (WORK MORE as opportunity cost of not working has risen)

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A rise in wages - When the wage is $15 your best choice of hours and consumption is at point A. The steeper line shows your new budget constraint when the wage rises to $25. Your feasible set has expanded.

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Point D on IC₄ gives you the highest utility. At point D, your MRS is equal to the new wage, $25. (MRS=MRT=w) You have only 17 hours of free time, but your consumption has risen to $175

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The dotted line shows what would happen if you had enough income to reach IC₄ without a change in the opportunity cost of free time (like birthday gift, not a wage increase). You would choose C, with more free time. (INCOME EFFECT)

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�The rise in the opportunity cost of free time makes the budget constraint steeper. This causes you to choose D rather than C, with less free time. This is called the substitution effect of the wage rise. (SUBSTITUTION EFFECT) (MRT rises with increase slope of feasible frontier, so MRS rises in move from C to D until D where the rate at which the worker is prepared to substitute reduced free time for increased consumption (MRS) = the increased MRT = wage�

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The overall effect of the wage rise depends on the sum of the income and substitution effects. In this case the substitution effect is bigger, so with the higher wage worker will take less free time and consume more at D

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The Income Effect and Substitution effects summary

income effect (more income is achieved so reduce work and free time rises)

- the effect that the additional income would have if there were no change in the price or opportunity cost (as if MRT remains constant at higher income

- hypothetical upward shift in feasible frontier / budget constraint

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substitution effect (higher wage / MRT / opportunity cost of free time so free time falls)

- A wage rise means that the wage earner loses more income for every one hour NOT worked.

- As a result, worker is less willing to sacrifice consumption for extra free time, since the opportunity cost of free time is higher.

- This means that their marginal rate of transformation (MRT) is higher.

- The wage earner responds to increases in the opportunity cost of free time by taking less free time.

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Is this realistic?�Do people think about MRS and MRT every day?

Economic theory helps to explain what people do

• Billions of people organize their working lives without knowing anything about MRS and MRT. So how can this model be useful?
• Remember from Unit 2 that models help us ‘see more by looking at less’. Lack of realism is an intentional feature of this model, not a shortcoming.
• Economists do not actually claim that people actually think through these calculations (such as equating MRS to MRT) each time we make a decision.
• Rather models works “as if” people make such calculations – like a pool player does not calculate the physics and work out the geometry to sink the ball but does it as if he or she is doing the calculations)

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• Trial and error replaces calculations
• Different people each try various choices (sometimes not even intentionally) and tend to adopt habits, or rules of thumb that make them feel satisfied and avoid regret. Eventually we could speculate that they might end up with a decision on work time that is close to the result of our calculations.
• The influence of culture and politics
• Although individual workers often have little freedom to choose their hours, it may nevertheless be the case that changes in working hours over time, and differences between countries, partly reflect the preferences of workers.

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Worldwide Working Hours�How do countries decide how much to work?

Working hours have changed over time…

• From the late nineteenth century (1800s) until the middle of the twentieth century (1900s), working time in many countries gradually fell from about a 60 hour week to between 30 and 40 hour weeks

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In South Africa?

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• South Africa’s Basic Conditions of Employment Act 75 of 1997
• Your employer is not allowed to require or permit you to work more than:
• 45 hours a week.
• Nine hours in a day if you work on 5 days or less a week.
• Eight hours in a day if you work more than 5 days a week.
• You must have a meal interval of 60 minutes after five hours of work. This may be reduced to 30 minutes by written agreement.
• Your lunch break may also be done away with by written agreement if you work less than 6 hours a day.

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Possible feasible sets and indifference curves

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• We can use the model and the concepts we’ve learned so far to help interpret political, legislative and historical change.
• For example, we can interpret the change between 1900 and 2013 in daily free time and goods per day for employees in the US using our model. The solid lines show the feasible sets for free time and goods in 1900 and 2013, where the slope of each budget constraint is the real wage.
• Assuming that workers chose the hours they worked, we can infer the approximate shape of their indifference curves:

The Income Effect over the 20^th century in the US

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• Before 1900, low consumption levels meant that workers’ were less willing reduce consumption for increased free time. (Flatter Indifference curves low MRS)
• But by the late 1900s and early 2000’s, workers had a higher level of consumption and valued free time relatively more — steeper indifference curve and higher
• From 1900 to 2013 an income effect is visible. In the shift from A to C the income effect of the wage rise, meant that workers reduced their working hours each day and took more free time.

The Substitution Effect over the 20^th century in the US

• At the same time, workers were more productive and were paid more, so each hour of work brought more rewards than before in the form of consumption, increasing the incentive to work longer hours.
• The rise in the opportunity cost of free time caused US workers to choose D rather than C, with less free time.

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Preferences can also change over time

• Over time, people change their preferences and can value consumption more or less than they did before, because of personal, cultural, political and economic changes.
• Popular culture, fashion and trends such as trying to “keep up with the Joneses” can also influence people’s spending behaviour.

conspicuous consumption

The purchase of goods or services to publicly display one’s social and economic status.

• https://core-econ.org/the-economy/book/text/50-02-glossary.html#glossary

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• People’s preferences will continue to change in future and different economies will change in different ways…

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Comparing countries

• We can use our model to understand the differences between the countries. The solid lines show the feasible sets of free time and goods for the five countries.
• Notice that the indifference curves for the US and for South Korea cross. This means that South Koreans and Americans must have different preferences.
• Point Q is at the intersection of the indifference curves for the US and South Korea.
• At this point Americans with higher MRS are willing to give up more units of daily goods for an hour of free time than South Koreans.
• Or Koreans with lower MRS are less willing to give up consumption for free time.
• (NB indifference curve for one particular country cannot interest in this way).

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Main points again

• People’s preferences with respect to goods and free time are described by indifference curves.
• Their production function (or budget constraint) determines their feasible set.
• The choice that maximizes utility is a point on the feasible frontier where the marginal rate of substitution (MRS) between goods and free time is equal to the marginal rate of transformation (MRT).

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• An increase in productivity or wages alters the MRT, raising the opportunity cost of free time.
• This provides an incentive to work longer hours (the substitution effect). But higher income may increase the desire for free time (the income effect).
• The overall change in hours of work depends on which of these effects is bigger.

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