The problem of scarcity

• Scarcity is a basic problem in economics.
• Scarcity is the fundamental economic problem of limited resources versus unlimited wants, which forces individuals, businesses, and governments to make choices.
• Microeconomics develops model to show how people make choices when they cannot have all of everything that they want, such as goods and free time.
• People face a trade off - in order to get more of x they will necessarily get less of y (if x ↑ then y↓), (if both x ↑ and y ↑ then there is no trade-off)
• A trade-off is the necessary consequence of scarcity because there are not enough resources to get everything
• Scarcity creates the need for trade-offs, and the best option forgone is known as the opportunity cost. 

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The trade-off between earnings and free time

• The example will be of a young person Karim who has a trade off between the amount of money he earns and the amount of free time he can enjoy
• To get more money he must have less free time (if x ↑ then y↓),
• To get more free time he must earn less money (if y ↑ then x ↓),
• How do we model how Karim chooses the combination of free time and consumption that is best for him?

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Assumptions

• Karim’s income y = wh, where:
• w is his wage of €30 an hour
• h are the hours worked (to a maximum of 16 hours a day as he needs time to eat and sleep)
• The slope of the line is constant (w = 30 as each extra hour adds 30 to his income) so Karim’s production function is linear (no diminishing marginal returns)
• Karim’s maximum earnings (and related consumption) are y = 30 x 16 = 480

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Karim wants more of both x and y �(not maximum x or maximum y)

• But Karim does not choose his maximum possible income/consumption as he values both income/consumption and free time
• He faces a scarcity which results in a trade off - the more free time he takes the lower will be his income/consumption
• So how does Karim choose the number of hours to work?
• We have to develop a model that brings together:
• Karim’s subjective preference for consumption and free time
• Karim’s objective feasibility constraint presented by the trade-off income/consumption and free time

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Karim’s subjective preferences and indifference curves

• Assumption 1 – Karim wants more of both goods (consumption and free time)
• Assumption 2 – Karim faces a trade off the more consumption the less free time, and the more free time the less consumption
• Key question 1: what are his subjective/personal preferences i.e. how much consumption is he willing to give up to have more free time and how much free time is a he willing to give up to have more consumption?
• Key question 2: How much does he value the two goods relative to each other?
• Answer: Is shown in Karim’s indifference curves which are (1) negatively sloped due to the trade-off between x and y, and are (2) non-linear as the relative value of x and y changes as he has more and less of x and y

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Karim’s preferences

• with free time on the horizontal axis and consumption on the vertical axis
• every point in the diagram represents a different combination of free time and consumption spending
• which combinations would he prefer if he could have them
• he prefers A to B because at A and B he consumes about 500, but he has more free time at A than at B
• he prefers D to C, both have about 20 hours free time, but consumption is higher at D
• Conclusion: Karim will always prefer to be on a higher indifference curve the further away from the origin the higher will be the combinations of the goods x and y i.e. higher combinations of free time and consumption

Drawing the indifference curve

• If you ask Karim and says he is equally satisfied at A and D
• He says he is indifferent between A and D and has equal utility (satisfaction) at both of these points
• Then you can draw an indifference curve through points A and D
• The indifference curve goes through A, E, F, G, H, and D as Karim is equally satisfied with combinations of free time and consumption at each of these points
• The indifference curves going through B and C are lower (closer to the origin) and Karim would be less satisfied to be on those indifference curves than he is to be on the highest indifference curve

Drawing the indifference curve

• We could ask Karim another question: ‘Imagine that you could have the combination at A (15 hours of free time, €540). How much consumption, in euros, would you be willing to sacrifice for an extra hour of free time?’
• Suppose he answers ‘€94’. Then we know that he is indifferent between A and E (16 hours, €446).
• Then we could ask the same question about combination E, and so on until point D.
• Karim is indifferent between A and E, between E and F, and so on, which means he is indifferent between all of the combinations from A to D.

Properties of indifference curves

• Indifference curves slope downward due to trade-offs: If you are indifferent between two combinations, the combination that has more of one good must have less of the other good.
• Higher indifference curves correspond to higher utility levels: As we move up and to the right in the diagram, further away from the origin, we move to combinations with more of both goods.
• 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: As a person can’t have different levels of utility with the same combination of goods
• As you move to the right along an indifference curve, it becomes flatter. The indifference curve is non-linear due to a declining Marginal Rate of Substitution

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Marginal rate of substitution (MRS)

• At A with 15 hours of free time and €540 of consumption, Karim would be willing to sacrifice €94 of consumption for an extra hour of free time, taking him to E (he is indifferent between A and E).
• His marginal rate of substitution (MRS)⁠ between consumption and free time from A to E is 94; it is the reduction in his level of consumption that would keep Karim’s utility constant following a one-hour increase of free time.
• At H with 19 hours of free time and €282 of consumption, Karim would be willing to sacrifice €32 of consumption for an extra hour of free time, taking him to D (he is indifferent between H and D).
• His marginal rate of substitution (MRS)⁠ between consumption and free time from H to D is 32; it is the reduction in his level of consumption that would keep Karim’s utility constant following a one-hour increase of free time.
• As such his marginal rate of substitution (MRS)⁠ his fallen from MRS = 94 to MRS = 32, as such the slope of the indifference curve becomes less steep as MRS falls

Intuition as to why indifference curves are non-linear (if they were linear the MRS would be constant and the amount of free time traded for consumption would stay constant)

• Intuition as to why indifference curves becomes flatter as you move along them to the left:
• the more free time and less consumption a person has, the less willing they will be to sacrifice further consumption in return for free time, so MRS will fall
• as you moves down the indifference curve to the right MRS falls i.e. the amount of consumption a person will be prepared to give up is less the more free time the person has and the less consumption they have
• What about the other way, as you move up along the indifference curve to the left?
• Each reduced level of free time (when moving to the left and there is less and less free time) will require an increasing amount of consumption to compensate for lost free time to maintain equal utility along IC, as such MRS rises
• In brief, the more you have of a good, the more willing you are to trade it for the other.

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MRS rises at x when indifference curve shifts upwards

• As you move up the vertical line through 15 hours, the indifference curves get steeper: the MRS increases
• For a given amount of free time, Karim is willing to give up more consumption for an additional hour when he has high consumption, compared to when his consumption is low
• By the time you reach A, where his consumption is €540, the MRS is high; consumption is so plentiful here that he is willing to give up €94 for an extra hour of free time.

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MRS falls at y when indifference curve shifts upwards

• If you fix consumption and vary the amount of free time i.e. if you move to the right along the horizontal line for €282, the MRS becomes lower at each indifference curve.
• This is because as free time becomes more plentiful, Karim becomes less and less willing to give up consumption
• Note: that the MRS is a positive number, while the slope of the indifference curve is negative i.e. to be precise, the MRS is equal to the absolute value of the slope

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Calculation of MRS

• The MRS / slope between A and E is 94 : At A with 15 hours of free time and €540 of consumption, Karim would be equally satisfied to sacrifice €94 of consumption for an extra hour of free time at E
• The MRS / slope at point A is calculated as follows:

The highest indifference curve is expressed by the following utility function u_o = (t, c) where u_o = (t - 6)²(c – 45) for t > 6 and c > 45

At E where c = 446 and t =16, u_o = 100 x 401 = 40 100 ( subject to rounding errors as whole numbers are used u_o is equal at E, A, H and D)

Rearrange as c = (u_o / (t - 6)²) + 45

Differentiate to find the slope dc/dt = -2u_o / (t - 6)³)

Substitute in u_o : dc/dt = -2(t - 6)²(c – 45) /(t - 6)³

Simplify dc/dt = -2(c – 45) /(t - 6)

MRS is absolute value so MRS = 2(c – 45) /(t – 6)

MRS at point A = 2(540 – 45)/(15 – 6) = 110

MRS at point D = 2(250 – 45)/(20 – 6) = 29.29

(MRS decreases from A to D)

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Karim’s objective feasible frontier

• Karim faces a trade-off - the more hours of free time (t) he takes, the less consumption (c) he can have
• Free time has an opportunity cost.
• Karim’s level of consumption is given by c = w(24 – t), where wage (w) = 30
• As t increase c falls
• At t = 24 hours of free time, c = 0
• max free time minimum consumption
• At t = 8 hours of free time c = 30 (24 – 8) = 480
• 16 hours of work per day is the maximum hours of work as he needs to rest
• c = w(24 – t) is Karim’s budget constraint as it indicates how much he has in his budget for consumption
• This is not subjective i.e. is is not based on his preferences – it is an objective constraint based on the wage (w) and the maximum number of hours he can work

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The Slope of the feasible frontier (MRT)

• Slope = △y / △x
• Slope = -30/1 = -30
• At any point on the feasible frontier, if free time increases by one hour, the maximum possible consumption decreases by €30 — so the slope is –30
• The absolute value of the slope of the feasible frontier is known as the Marginal Rate of Transformation (MRT)
• As a one hour decrease in free time (t) is transformed into 30 units of consumption (c)
• If the wage increases e.g. to €35 per hour, then the slope becomes steeper and the MRT rises

Points on and around feasible frontier

• Points on the feasible frontier – to move from one point to another along the feasible frontier there must be a trade off
• More consumption is due to less free time, or
• More free time leads to less consumption
• Point C is not feasible (no point above the feasible frontier is possible eg if 11 hours of free time are taken then c = 30 (24 – 11) = 390 units of consumption, 430 units of consumption is not possible with a wage of 30 per hour
• Point D is feasible, but it is not optimal as if t = 20 then c = 30 (24 – 20) = 120 units of consumption, but only about 80 units are consumed at D
• At D he would consume less than he earned – perhaps you loses part of his payment or is not paid in full – and it is assumed that he only cares about his consumption and free time so he has no other use for his earning
• At D Karim does not face a trade off as he can consume more (up to 120 units) without reducing his free time of 20 hours
• The shaded area is called the feasible set

Marginal theory of decision making

• We have now identified two trade-offs:
• The marginal rate of substitution (MRS) measures the trade-off that Karim is subjectively willing to make between consumption and free time.
• The marginal rate of transformation (MRT) measures the trade-off that Karim is objectively constrained to make by the feasible frontier.
• Karim chooses between his consumption and his free time by striking a balance between these two trade-offs (where MRS = MRT is optimal).

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Optimal decision making under scarcity

• Indifference curves describe Karim’s subjective preferences for different combinations of consumption and free time (shows the trade-off he is willing to make)
• Feasible Frontier indicates which combinations are objectively a feasible budget constraint for Karim (shows the trade-off he is constrained to make)
• Next step bring the indifference curve and feasible frontier together to determine the combination of consumption and free time that will be chosen

Optimal decision making under scarcity

• Highest indifference curve is IC4, but it is not feasible to achieve any combination of c and t along IC4
• At B, Karim could achieve a better combination of c and t at any point above IC1 and below the feasible frontier
• At C and D (which have equal combined utility of c and t for Karim) Karim could achieve a better combination of c and t at any point above IC2 and below the feasible frontier
• At E – this is the highest combined utility of c and t for Karim that is feasible, this is where IC3 is a tangent to the feasible frontier
• IC3 and the feasible frontier intersect at a single point E as such IC3 is the highest feasible indifference curve which gives Karim the highest feasible combined utility of c and t
• At E, Karim chooses 17 hours of free time (t) and 210 units of consumption (c) (he chooses to work for 7 hours per day)
• At E - MRS = MRT

Optimal outcome at E MRS = MRT

• The slope of the indifference curve represents the MRS: It is the trade-off he is willing to make between free time and consumption.
• The slope of the frontier represents the MRT: It is the trade-off that he is constrained to make between free time and consumption because it is not possible to go beyond the feasible frontier.
• At B and D MRS > MRT
• At B MRS is 223 and MRT is 30; At D MRS is 105 and MRT is 30
• At B and D Karim’s subjective preference to increase free time even at the relatively high cost of lost consumption is indicated by STEEP SLOPE (high MRS at B and D) (steeper slope = higher MRS cost he is subjectively prepared to pay to increase free time)
• Karim’s objective ability to increase consumption at a relatively low cost in terms of lost consumption is indicated by LESS STEEP SLOPE (low MRT at B and D) (less steep slope = lower MRT costs he objectively has to pay to increase free time)
• Therefore, at B and D Karim has an incentive to increase his or her free time as he is subjectively prepared to sacrifice more consumption (c) for additional free time (t) (MRS) than he is objectively required to sacrifice c for t as per MRT which is equal to the lost wage per unit of additional t (as indicated by MRS > MRT) 
• At B and D the opportunity cost of free time in the form of lost consumption (MRT) is lower than the cost that Karim is prepared to pay for free time in the form of lost consumption (MRS) (MRT < MRS)
• Therefore, Karim will continue demanding more free time and lower consumption (moving from B to D to E) and each time will be gaining more utility as he will be on a higher indifference curve
• At E: the point on the feasible frontier where the indifference curve and the feasible frontier have the same slope,
• At E: the cost he is prepared to pay for increased free time MRS (30) is equal to the cost he is required to pay for increased free time MRT (30)

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Optimal outcome at E MRS = MRT

• At A, the MRT > MRS, MRT is 30 and MRS is 2
• At A MRS is low indicating that Karim is subjectively prepared to give up an hour of free time even for a small increase in consumption (2 units)
• Objectively MRT is higher than MRS, so if he gives up an hour of free time he will receive 30 additional units of consumption
• So at A Karim will have an incentive to reduce his free time
• At A what he subjectively requires for a reduction in free time (2 units of c) is less than the 30 extra units of c that he will in fact gain from reduced free time
• Therefore, Karim will continue reducing his free time from A until he reaches point E where the amount of c he subjectively requires for reduced free time (MRS) is equal to the amount that he does gain (MRT)
• To the left of E, Karim would require more than 30 units of extra consumption to give up an hour of free time (MRS > 30) and that is not feasible as MRT = 30 (as per the level of the wage)
• So the optimal outcome is at E where MRS = MRT

Constrained choice or constrained optimisation problems

• Karim’s decision on working hours is what is called a constrained choice problem⁠ or constrained optimisation problem
• a decision-maker pursues an objective (utility maximization, in this case) subject to a constraint (his feasible frontier).
• Both free time and consumption are scarce for Karim because:
• Free time and consumption are goods: Karim values both of them.
• Each has an opportunity cost: More of one good means less of the other.
• In constrained choice problems, the solution is the choice that best satisfies the individual’s objectives.
• If we assume that utility maximization is Karim’s goal, then the best combination of consumption and free time is a point on the feasible frontier at which MRS = MRT (as absolute values)
• If MRS ≠ MRT he can improve his combined utility by increasing or decreasing levels of free time and consumption

Calculation of max combined utility u (t,c)

• Karim’s Indifference Curves are expressed by the utility function: 𝑢(𝑡,𝑐)=(𝑡−6)²(𝑐−45) for 𝑡>6,𝑐>45
• Karim’s Feasibility Frontier is expressed by the budget constraint: 𝑐=𝑤(24−𝑡)
• Substitute c into his utility function as follows: 𝑢=(𝑡−6)²(𝑤(24−𝑡)−45)
• Maximise this expression with respect to t by equating its derivative to 0 (using the product rule): 𝑑𝑢/𝑑𝑡=2(𝑡−6)(𝑤(24−𝑡)−45)−𝑤(𝑡−6)² = 0

⇒2(𝑤(24−𝑡)−45)=𝑤(𝑡−6)��Solve for t: 𝑡=18−30/𝑤

As wage w = 30, t = 18 - 30/30 = 17

So maximum utility occurs at E where:

t = 17 (hours of free time or 7 hours worked), and

c = 30(24-17) = 210 (or €210 of consumption)

(you can use the second derivative to confirm that this is a maximum not a minimum)

So maximum combined utility 𝑢(𝑡,𝑐) for Karim, given the budget constraint, occurs at point E where MRS = MRT�

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Another method for calculating of max combined utility u (t,c)

• For 𝑢(𝑡,𝑐)=(𝑡−6)²(𝑐−45) for 𝑡>6,𝑐>45
• As MRS can be expressed as equal to the ratio of the marginal utilities du/dt and du/dc
• du/dt is 2(𝑡−6)(𝑐−45)  (marginal utility of free time)
• du/dc is (𝑡−6) ² (marginal utility of consumption)
• MRS=2(𝑐−45)/(𝑡−6)
• At E the two conditions satisfied by Karim’s best outcome are:
• 𝑐=𝑤(24−𝑡) (max utility is on the budget constraint)
• 2(𝑐−45)/(𝑡−6)=𝑤 (max utility is where MRS=MRT)
• Solve simultaneous equations for t given that w = 30:
• Solution t = 17 and c = 210 at E��

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Impact of different weightings of preferences for c and t

• If Karim weights free time (t) and consumption (c) equally then his indifference curve will by shaped like a simple hyperbola where constant utility (u) along indifference curve is given by u = c x (t - 8), t>8
• then optimal outcome will be at point X half-way on the y axis (at 240 units of consumption) and half-way between 8 and 24 on the x axis (i.e. 16 hours of free time) which gives 240 x (16-8) = 1920 unweighted utility units)
• if t and c are equally weighted this mid point along the feasible frontier will always give the maximum combined utility as compared to any other point on the the feasible frontier e.g. at X combined utility is 1920, at A = 60 x (22-8) = 840 and at D = 360 x (12 – 8) = 1440)

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• If Karim weights free time (t) more than consumption (c) then the combined utility is indicated by an indifference curve such as the following 𝑢(𝑡,𝑐)=(𝑡−6)²(𝑐−45) for 𝑡>6,𝑐>45
• Given the budget constraint 𝑐=30(24−𝑡) the maximum combined utility is at a point E with 17 hours of free time and 210 units of consumption
• if unweighted the utility units at E would be (17-8) x 210 = 1890 utility units
• but the 17 hours of free time have a higher weighting so combined utility is (17-6)² x (210-45) = 19965 weighted utility units at E along IC3
• at X (the mid point) combined utility would be calculated as follows (16-6) ² x (240-45) = 19500 weighted utility units, this is below the maximum combined utility and would be indicate on the diagram by a lower indifference curve below the highest feasible curve at IC3

X (mid point) at 16, 240

E at 17, 210

Max utility is at X for unweighted utility function

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Max utility is at E for utility function weighted in favour of free time (t²)

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Technological progress and rising wages

• What will be the impact of a rising wage for Karim from €30 per hour to €45 per hour?
• Karim’s rising wage will cause the feasible frontier (budget constraint) to swivel upwards)
• At 24 hours of free time (t) – consumption (c) continues to be 0 as 𝑐=45(24−𝑡)
• At 8 hours of free time (t) consumption (c) rises from 480 units to 720 units as 𝑐=45(24−𝑡)
• c = 45(24-8) = 720 units
• Due to the new wage, the slope of the feasible frontier changes from -30 to -45, so MRT rises to 45

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What will Karim do when wages rise?

• Karim will be able to move to the highest possible indifference curve that is tangential to the new feasible frontier – he will be at F rather than E
• On a higher indifference curve Karim will be better of due to the wage (w) increase from €30 per hour to €45 per hour
• At F the MRS = MRT and MRT = w, so MRS = MRT = w
• At F he has slightly more free time and he has higher consumption due to the increased wage – but this is only one of the possible outcomes, depending on his preferences Karim may choose to take less free time and higher consumption when his wage rises
• To predict which outcome will occur we need to understand the income effect and the substitution effect when w rises
• At F the income effect dominates as Karim consumes more and takes more free time.

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Income effect and substitution effect

• The increase in wage (w) affects Karim in two ways.
• The income effect The income effect of a wage rise makes Karim want to take more free time
• As his income rises his feasible set expands and he will be able to consume more
• The extra consumption will allow him to consume more even as he takes more free time (he has enough income and he may feel that he can work less time)
• The substitution effect of a wage rise makes Karim want to take less free time.
• the wage rise increases the opportunity cost of free time, giving Karim a greater incentive to work
• taking an extra hour of free time now costs more in lost consumption encouraging him to work more
• If wages rise Karim is always better off (on a higher indifference curve with higher u(t,c), but there are two effects of a wage rise on work time/free time, which act in opposite directions
• When wage rises – income effect makes him wish to work less and substitution effect makes him wish to work more (depending on his preferences for the overall or net effect - either effect could dominate so he may take more or less free time in response to a wage increase)

Income effect

• If someone has an additional lumpsum income of 1000 units which is like a gift and is not linked to time worked
• Then the feasible frontier/budget constraint will shift upwards by 1000 units
• The result will be a shift to B, either:
• First case: The amount of free time will increase and consumption increase (if the person has a relatively strong preference for free time and happy to gain less c for a unit increase in t so indifference curve is less steep), or
• Second case: The amount of free time will stay the same and consumption will increase (if the person has a relatively strong preference for consumption and requires the gain of more c for a unit increase in t so indifference curve is more steep),
• Note: The amount of free time will never be decreased in response to lumpsum income as there is no increase to the opportunity cost of free time as the wage (slope MRT) has not changed

Substitution effect

• When wage increases the feasible frontier/budget constraint pivots upwards
• Why – at 70 days of free time c is still zero, but for every other number of days of free time 130 units are earned per day of work (instead of 90 units) so earning and consumption increased for each day worked
• At D the person has responded to the higher real wage by reducing their free days and increasing the amount of time they work
• In this case the substitution effect is dominant (is bigger than the income effect) as the person responds to the higher opportunity cost of not working due to the higher wage
• At D MRS = new MRT (= higher wage of 130)
• MRT is higher than at A (due to the increased wage so the rate of transformation of reduced free time into consumption has increased)
• At D MRS is higher than at A as:
• Generally, for a given t, MRS will be steeper on higher indifference curve as the amount of c is higher relative to t and person will be willing to substitute more c for t
• Similarly Upward movement along IC4 will lead to higher MRS as the amount of c is higher relative to t and person will be willing to substitute more c for t

Originally c = 90(70-d)

Then wage increases from 90 to 130

Now c = 130(70-d)

Decomposition

• Decomposition can be used to identify income effect and substitution effect more precisely
• Step 1: At A then wage increases from 90 to 130 feasible frontier pivots up
• Step 2: Results in move to D tangent of IC4 and new feasible frontier, where MRS = new MRT (w = 130)
• Step 3: Isolate income effect by drawing a line showing increased income with original MRT that is tangential to IC4 i.e. dotted line shows what would happen if person had enough income to reach IC₄ without a change in the opportunity cost of free time (no change in wage) where point C would be chosen with higher c and free time
• Step 4: Isolate substitution effect where IC4 is tangential to new steeper feasible frontier, the rise in the opportunity cost of free time (w = 130) makes the budget constraint steeper and person chooses D with less free time and higher consumption
• Step 5: The overall effect of the wage rise depends on the sum of the income and substitution effects. In this case, the negative substitution effect is bigger, so with the higher wage the person takes less free time.

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The income effect (because the budget constraint shifts outwards): the effect that the additional income would have if there were no change in the opportunity cost

The substitution effect (because the slope of the budget constraint, the MRT, rises): the effect of the change in the opportunity cost, given the new level of utility.

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Net effect depends on a person’s preferences or situation

• Whether the substitution effect is big enough to outweigh the income effect depends on the person’s preferences or situation regarding the substitution between working time and consumption (related to slope of IC curve - MRS).
• If MRS is low (IC relatively flat) then substitution effect is more likely to dominate
• e.g. a student during the holidays might be prepared to give up quite a lot of free time to gain more for consumption (relative preference for consumption)
• the substitution effect dominates as the student is relatively prepared to give up more free time to get an extra unit of consumption
• If MRS is low then 1 unit increase in consumption (△c) is compensated for by a relatively large decrease in free time (△t2)
• The reason this is described as a low MRS is because a one unit decrease in free time (△t) is associated with a relatively low increase in consumption (△c1) (as slope of MRS is given by change on y axis i.e. △y/ △x))
• If MRS is relatively low and IC relatively flat, when wage increases then the amount of free time will fall (to D)

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• If MRS is high (IC relatively steep) then income effect is more likely to dominate and when wage increases amount of free time will increase
• e.g. a person with many domestic responsibilities, giving up free time may be more difficult and they would only be prepared to give up a small amount of free time for an additional unit of consumption
• the person’s relative preference for free time is indicated via a relatively steep IC
• If MRS high then 1 unit increase in consumption (△c) is compensated for by a relatively small decrease in free time (△t1)
• MRS is high as on Y axis small △t leads to a large △c , as m = △y/ △x
• If MRS is relatively high and IC relatively steep, when wage increases then the amount of free time will likely rise as the wage rises as the income effect will dominate the substitution effect

• Note:
• This is not about comparing the impact of two different relative weights between c and t in the utility function u(c,t) to predict that the optimal point of tangency with a specific feasible frontier will be to the right of (and below) the mid-points if free time has a relatively higher weighting than consumption, as per 𝑢(𝑡,𝑐)=(𝑡−6)²(𝑐−45) as compared to u = c x (t - 8)
• This is about comparing the impact on c and t when there are two different feasible frontiers as the wage rises showing that
• For individuals who have a relatively low MRS (flat IC), and a relative preference for consumption, will give up give up more free time to get an extra unit of consumption the substitution effect will dominate, and
• For individuals who have a relatively high MRS (steep IC), and a relative preference for free time, will give up less free time to get an extra unit of consumption the income effect will dominate

Differing preferences across nations

• Drawing indifference curves suggests that Dutch and American workers also have different preferences.
• The Dutch indifference curve is steeper than the one for the US.
• This means that at the same amounts of daily goods and hours of free time (indicated by point Q), the Dutch place a higher value on free time relative to goods than do the Americans.
• The slope of the indifference curve is the MRS, that is, how much a person values free time compared to how much they value goods (MRS is steep so Dutch must gain a lot of consumption for loss of free time values free time).
• This is consistent with the observation that Americans work long hours compared to the people of the Netherlands and most other equally rich nations.
• Preferences differ among people, with the people of different nations and cultures having different indifference curves.

Model operates on assumption of ceteris paribus (i.e. what is the impact of a higher wage on consumption and free time chosen holding other things constant)

• The model of Karim’s decision making leaves out important factors that influence decisions about working hours
• It assumes that workers only care about two goods, free time and consumption.
• But they may also care—for example—about their future career, and work longer hours to gain valuable experience and opportunities for promotion.
• Or their decision may depend on the other demands on their time: for example on how many children they have and the availability of childcare.
• For example, it might be the case ceteris paribus that if an employer raises wages, the employees would like to increase their work hours (and reduce free time – due to dominance of substitution effect), but if the employer closed the workplace nursery at the same time, the wage rise might not have the same effect

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The Veblen effect

• Thorstein Veblen developed a concept of conspicuous consumption which can help us understand how working hours have changed over time
• The Veblen effect states that the more rich people consume, the longer other people will work, so as to try to copy (as best they can) the standards of the rich
• As a result, we would expect people to work longer hours in countries in which the rich are especially rich, and people to work less where the rich are only modestly richer than the rest.

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• Note: The most important element for the decline in work hours in the twentieth century is that voting rights were extended to include most adults early in the century. When overworked employees got the right to vote, in virtually all countries their trade unions and political parties demanded reductions in working hours.

The figure shows that a larger share of income going to the very rich is associated with longer average working hours.

A decline in the relative incomes of the very rich in a particular country is closely associated with the decline in work hours in that country eg Netherlands (work the least hours) and Sweden (although more recently working hours have increased as inequality has risen in Sweden and US)

Gender wage gap

• Almost everywhere in the world, women are less likely than men to do paid work. Women who work for pay do fewer hours than men, on average.
• We know from our model that wages are an important factor in workers’ decisions on working hours.
• It is possible that women make different choices because their rewards from undertaking paid work are lower, due to discrimination in the labour market.
• Lower wages for women give them a reduced incentive to work (the substitution effect), but the income effect works in the opposite direction.
• If the substitution effect dominates, it is possible that lower wages could lead women to choose lower hours. 
• But given the significant size of gender wage and working hours gaps, a more compelling theory is based on the gender division of labour.

Gender Division of Labour

• Researchers have found that big differences between men’s and women’s work emerge when they have children. Women’s earnings fall substantially when their first child is born, and remain permanently lower than they were before. But the birth of a child makes almost no difference to the earnings of men.
• This suggests that we may observe a gender division of labour⁠ in families, with women more likely to undertake domestic work, particularly childcare. 
• Evidence from time use studies, in which people are asked to keep detailed time diaries recording their activities throughout the day. In every country for which we have data, men spend more time on paid work than women, but women spend more time on unpaid work than men.

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Scenario 1: Where Ana and Luis are paid the same wage (30) and both are able to work a max of 8 hours per day by law – their households optimal point is at B

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Scenario 2: Where due to gender discrimination Ana is paid a wage of 17 and Luis a wage of 30 – their household optimises at D, where Luis works for 8 hours of paid work per day and Ana does 2 hours of paid work per day – the unequal wages leads to a gender division of labour where Ana does more domestic work (12 hours) and Luis does more paid work (8 hours)

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The lower wage for Ana has a substitution effect: the opportunity cost of an hour of non-working time is now only $17, reducing the incentive to work and increasing the amount of non-working time.

It also has an income effect in the opposite direction: lower earnings lead the household to reduce the amounts of both goods.

But in this household model, with two wage-earners, the income effect is small: the change in Ana’s wage has no effect on the income from the eight hours worked by Luis. That is why the substitution effect dominates, and the paid hours worked by Ana fall from six to two.

Summary

1. Simple model of decision-making under scarcity

• Indifference curves represent preferences
• Feasible frontier/budget constraint represents choice constraints
• Utility-maximising choice where MRS = MRT

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2. Used model to explain effect of wage increase on labour choices

• Overall effect on free time = (+ve) Income effect + (-ve) Substitution effect

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• Next lecture - The role of social interactions in individual choice

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