Topic 2 Flashcards
To understand Labour Supply Decisions: The Income-Leisure Model Reservation Wages Income and Substitution Effects Individual Labour Supply Curves Overemployment, Underemployment and Overtime
What is the Basic Income-Leisure Model?
It tries to explain how individuals choose to devote time between Work and Leisure. Two main factors are used to predict time allocation under this model: Preference & Budget.
What’s the difference between Preference and Budget under the Basic Income-Leisure Model
Preference relates to how much a worker values consumption relative to leisure, while budget relates to how much time does the person have to work with or how much money do they give up if they work a little bit less.
How is a workers preference expressed mathematically?
- Expressed with utility function U = U(c, L)
- If U(c1, L1) > U(c0, L0), this means that the worker prefers c1 and L1 to c0 and L0.
- Example: U = cαL1−α, 0 < α < 1 (Cobb-Douglas) Gives us a way of ranking different bundles Workers have preferences over different combinations, or “bundles”
What is an indifference curve?
A curve on a graph (the axes of which represent quantities of two commodities) linking those combinations of quantities which the consumer regards as of equal value.
- We can represent preferences over different bundles of (c, L) graphically by using indifference curves.
- If bundles (c0, L0) and (c1, L1) are on the same indifference curve, the person is indifferent between them, or: U(c0, L0) = U(c1, L1). If bundle (c0, L0) is on a higher indifference curve than bundle (c1, L1), the person prefers bundle (c0, L0) to bundle (c1, L1), or: U(c0, L0) > U(c1, L1).
Why is marginal utility important to indifference curves?
Marginal Utility is additional utility a person gets from consuming a little more of something, holding everything else constant.
- when optimizing their utility, people will think about the tradeoffs they face: how much extra utility will they get if they trade a little bit of leisure for a little bit of consumption or vice-versa. Utility functions are assumed to exhibit diminishing marginal utility. Consuming more of something increases your utility (marginal utility is positive). But the more of it you consume, the less your utility increases (marginal utility is diminishing).
- In the context of the indifference curve: Your utility will increase a lot if your leisure time increases from zero to one hour. If you are already enjoying 23 hours of leisure, an extra leisure hour will still increase your utility, but not by that much. Similarly, if your level of consumption is very low, your utility will increase a lot if you are able to consume a bit more But if your consumption is already at a high level, the extra utility you get from a bit of extra consumption will be smaller.
- Importantly, the marginal utility tells you why indifference curves convex to the origin.
How is the Marginal rate of substitution related to the Basic Income-Leisure Model?
This is the rate at which a worker is willing to trade off between L and C to remain exactly as well off.
- Graphically, the MRS is the slope of the person’s indifference curve. At low levels of L, the indifference curve is steep; this means that the MRS is high. Why? At low L, the worker values L a lot, compared to c: MUL is relatively high; MUc is relatively low They are willing to give up a lot of c in exchange for a little L and remain at the same utility level As L increases, the curve becomes flatter; this means that the MRS becomes lower. Why?: As L increases, MUL becomes lower At high levels of L, the worker is willing to give up a lot of L in exchange for a little c and remain at the same utility level
Define Budget Constraint.
It determines the set of affordable (C,L).
Workers are constrained by a number of things:
- Worker has limited non-labour income (YN) .
- Wage worker can earn is (W).
- Only 24 hours in a day… Maximum number of units of time a person can work (hours, days, etc) is (T).
- This determines set of feasible combinations of (c, L).
**According to this model, total income must equal total expenditures. Thus, no savings or investments.**
What is the mathematical formula for the budget constraint?
C = W(T-L) +YN
W is the wage that the worker earns per hour.
T is the total number of hours available to the worker.
T − L is equal to the number of working hours.
YN is the worker’s non-labour income.
When graphing the budget constraint:
Maximum possible amount of consumption is (a) if leisure is equal to zero, i.e. if the worker works all T hours.
Maximum possible amount of leisure: (b)
If leisure is equal to T, consumption is equal to (c)
Slope of budget line: (d)
What does W imply?
a. WT+YN
b. T
c. YT
d. -W
W implies the that the “price” of an hour of leisure is the hourly wage W.
Define workers equilibrium and how it relates to the basic income-leisure model.
It is the point where the indifference curve is tangent to the budget line. No other feasible point can give the worker a higher level of utility.
Or mathematically, it is the point where MRS = W
The point of the basic income-leisure model is to determine the point that maximizes affordable utility.
What’s the difference between endogenous and exogenous variables with examples?
Workers choose their optimal bundle of consumption and leisure (endogenous variables) by maximizing their utility subject to their budget constraint.
The budget constraint depends on the total amount of time available to the worker, the hourly wage, and the worker’s non-labour income (exogenous variables).
So what choosen by the person (endogenous) vs what’s dictated to them (exogenous).
Are there cases where it is optimal for an individual to choose not to work? And what does this mean in the context of work participation?
YES! This would happen if we have a “corner solution”: the worker maximizes utility at the point where L = T.
- This type of worker would choose not to work
- Therefore they would be considered out of the labour force (non-participant)
Define reservation wage. And not its relationship to the cornering solution for out of labour.
The reservation wage is the lowest wage for which a worker is willing to work.
- If the wage is above the reservation wage, the worker optimally chooses a positive number of working hours.
- If the wage is less than or equal to the reservation wage, the worker will optimally choose to stay out of the labour force (work zero hours)
A worker’s reservation wage is equal to their MRS at the point where L = T
The reservation wage will depend on the individual’s preferences and their non-labour income
very important to know
How does an increase in non-labour income affect a worker’s labour supply decision?
Assuming that leisure is a normal good, an increase in non-labour income will reduce the optimal amount of hours that a worker wants to work.
- Assuming that leisure is a normal good, an increase in non-labour income will reduce the optimal amount of hours that a worker wants to work
- This is known as an income effect
A normal good is something consumed in a higher amount the higher one’s income increases. An inferior good is something that is less consumed the higher one’s income increases.
How does a wage increase affect a worker’s labour supply decision?
Two effects:
- A higher wage makes leisure more “expensive” relative to consumption ⇒ this is known as the substitution effect
- A higher wage makes the worker “wealthier” ⇒ income effect as before
How does a wage increase affect an individual who was not initially working?
- No income effect, because higher wage does not make the individual “wealthier”, given that they are not working.
- Substitution effect operates as before: leisure is more expensive, so the worker wants to reduce her leisure, increase her working hours and increase her consumption
⇒ A wage increase may induce entry into employment among individuals who were initially choosing not to work, if the new wage is above the individual’s reservation wage
Note also that a wage increase can never induce a worker to exit employment (even though it may induce a reduction of hours), because the wage will remain above the individual’s reservation wage
What is the individual labour supply curve?
- The labour supply curve plots the optimal choice of labour for every possible value of the wage.
- The labour supply curve will be upward sloping if the substitution effect dominates the income effect.
- As W increases, the worker supplies more hours of labour
3. The labour supply curve will be downward sloping if the income effect dominates the substitution effect. - As W increases, the worker supplies fewer hours of labour
4. The labour supply curve will be backward bending if the substitution effect dominates when wages are low, and the income effect dominates when wages are high
Define Underemployment and draw and example.
Refes to a worker who would like to work more hours given wage rate.
Define Overemployment and draw its graph.
Refers to a worker who would like to work fewer hours given wage rate.
in regards to overtime pay, why not simply pay the worker a higher wage, rather than paying an overtime premium?
Consider the “straight time equivalent wage”, that is, the equivalent average hourly wage that would allow the worker to earn the same total income.
The model shows that the overtime premium induces the worker to work more hours than the straight-time equivalent
True or False: Firms can induce workers to work more hours by paying an overtime premium?
True:
Overtime premium:
Wage W0 for the first X hours worked, then W1 > W0 for every additional hour.
