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- ECO1010F (ECO1010F)
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- University Of Cape Town (UCT)
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UNIT3ECO3 - (/) scarcity, work, and choice
Wednesday, June 23, 2021 12:15 PM How individuals do the best they can, and
How they resolve the trade-off between
Earnings and free time
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
Scarcity – the fundamental economic problem of having seemingly unlimited human wants and needs in a world of
limited resources.
Consumption good - A good or service that satisfies the needs of consumers over a short period.
Opportunity costs- When taking an action implies forgoing the next best alternative action, this is the net benefit of the
foregone alternative. (The unavoidable trade-offs in the presence of scarcity: satisfying one objective more means
satisfying other objectives less. Used when an individual has to make choices)
Economic cost- The out-of-pocket cost of an action, plus the opportunity cost.
Economic rent- A payment or other benefit received above and beyond what the individual would have received in his or
her next best alternative (or reservation option)
Accounting (keep track of MONEY) vs. Economics (takes into account preferences and enjoyment i.e. opportunity costs
and benefits associated with each alternative)
Concave: when a line joining two points on a curve lies entirely below the curve
Convex: when a line joining two points on a curve lies entirely above the curve
Tangency - When two curves share one point in common but do not cross. The tangent to a curve at a given point is a
straight line that touches the curve at that point but does not cross it.
•Average product
Hours of Work and Economic Growth: •AP = TP/N which implies TP = AP . N
• John Maynard Keynes (Economic Possibilities for our Grandchildren) = in 100 years’ time, technology
would have solved the economic problem (objected) •Marginal product
• NB! Technology influences production and standard of living = will shift TP and frontier expands (given •MP = ∆ TP / ∆ N which implies 〖TP〗_n=〖TP〗_(n-1)+ 〖MP〗_n
wider choice of combinations) and will be steeper (increased MP)
Production Function
- A graphical or mathematical expression describing the amount of output that can be produced by any given Average product - Total output divided by a particular input
amount or combination of input(s). The function describes differing technologies capable of producing the (e.g. total output divided by the total number of hours of labour put in or number of workers)
same thing The AP is the slope of a ray (a line from the origin to the TP curve)
Labour- an input in the production of goods and services. The AP decreases as more inputs are added
If working out average product and input is zero use a dash as it is undefined
Total product (TP): Total output plotted against the quantity of inputs • AP = TP/input
Average product (AP): (Total output/total inputs) plotted against the quantity of inputs
Marginal product (MP): Change in total output/change in total inputs) plotted against the quantity of inputs Marginal product - The additional amount of output that is produced if a particular input was increased by one unit,
while holding all other inputs constant.
We assume there is a positive relationship between studying and the final grade obtained. We call ceteris paribus assumptions - means ‘holding other things constant’
this relationship a production function. Student X is inputing study hours and outputing a grade - derivative of TP with respect to the input
- tangent at that point (slope of curve at that point of tangency)
• MP = slope of your TP curve
Diminishing marginal returns - A situation in which the use of an additional unit of a factor of production results in a
smaller increase in output than the previous increase.
• Law of diminishing marginal returns = graph is increasing, but at a decreasing rate (this occurs after the point of
inflection of your TP curve)
• NB! Time will always be on the x-axis with 24 Hrs being your MAXIMUM
- identify diminishing marginal returns is if the marginal product is less than the average product.
No opportunity cost if move from being inside the frontier, to being along the curve
ECO1010F Page 1
, Feasible frontier
- The curve made of points that defines the maximum feasible quantity of one good for a given quantity
of the other
Feasible set- All of the combinations of the things under consideration that a decision-maker could
choose given the economic, physical or other constraints that he faces. The area inside the frontier,
together with the frontier itself, is called the feasible set.
Marginal rate of transformation (MRT)- The quantity of some good that must be sacrificed to acquire
one additional unit of another good. At any point, it is the slope of the feasible frontier.
Indifference curve
A curve of the points which indicate the combinations of goods that provide a given level of utility to the individual.
Every point on the indifference curve has the same utility
Indifferent - equally satisfied with either outcome/combination (this occurs along the same indifference curve)
Preferences - A description of the benefit or cost we associate with each possible outcome.
Utility - A numerical indicator of the value that one places on an outcome, such that higher valued outcomes will be
chosen over lower valued ones when both are feasible.
• To describe preferences, we don’t need to know the exact utility of each option, we just need to know which
combinations provide more or less utility over others
Marginal rate of substitution (MRS)- The trade-off that a person is willing to make between two goods. At any point, this
is the slope of the indifference curve. It is the amount of one good you’d be willing to give up to obtain one more unit of
the other )
MRS is determined by the consumer’s preferences. As you move along the indifference curve the MRS changes. This
makes sense because when you re-evaluate how much of product Y you are willing to give up to obtain an extra unit of
product X, the answer depends on how much (or how little) of X and Y you have already.
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: Would lead to contradiction
• As you move to the right along an indifference curve, it becomes flatter because of the decreasing marginal rate of
substitution(sacrificing one for the other becomes less willing as you move down along the curve )
The convex shape of the indifference curve shows a decreasing marginal rate of substitution (MRS).
Indifference curves slope downwards due to trade-offs (increasing one good, will decrease the consumption of the
other)
This TP function is convex up to the point of inflection and concave thereafter
The law of diminishing returns sets in where MP is at its maximum (and TP has its inflection point)
Decision making and scarcity: (Which combination will indeed be chosen?)
• Indifference curves = indicate preferences & slope shows trade-offs willing to AP and MP are the same where the slope of the ray to the TP curve is equal to the slope of the tangent to the TP curve
make
• Frontier = constraint on choice & slope shows trade-off constrained to make Where the TP curve becomes negatively sloped, MP becomes negative
• Maximization of utility: where indifference curve is tangent to frontier and MRS =MRT
• Above equilibrium: MRS>MRT, and Below equilibrium: MRS<MRT The utility-maximising choice is where the amount of one good the individual is willing to trade-off for the other good
(MRS) equals the actual trade-off between the two goods (MRT) MRS = MRT → Op mal
• Constrained choice problem - how we can do the best for ourselves, given our
preferences and constraints, and when the things we value are scarce (pursuing an
objective, subject to a constraint)
• Assumption = utility maximization is main goal of individuals Note that MRS is highest when we have a lot of the good on the y-axis and lowest
when we have a lot of the good on the x-axis. What does this tell us? It basically
constrained optimization problem means that when you have a lot of good y, you are willing to give up a lot of it for
Problems in which a decision-maker chooses the values of one or more variables to achieve an objective a little bit of x and when you have a lot of x you are not willing to give up much y
(such as maximizing profit) subject to a constraint that determines the feasible set (such as the demand for more x.
curve).
The Budget Constraint
An equation that represents all combinations of goods and services that one could acquire that exactly exhaust one’s
budgetary resources.
• Slope = wage rate = MRT = opportunity cost of free time (MRS) (optimal set) Indifference curves show how much people like things and what they are willing to exchange of one product to get more
• Area under budget constraint = feasible set of another product (i.e. their preferences)
• Budget constraint: c = w(24-t) We use a budget line to show the combinations of products a person can buy with the money that they have available to
Consumption(c) is dependent on your income spend (their budget constraint).
t= free time
Wage rate- the rate of compensation for a worker. It is one of the central themes of the study of human resources. It
is determined by 2 factors: productivity at work or number of production hours. If the consumer’s income increases, but prices are the same, then the budget line will shift parallel outwards. The slope
will remain the same, because the relative prices of X and Y (i.e. PX/PY) have not changed. But, with a bigger budget, the
Pivots/rotates rather than parallel because 24 hour hours in a day amount of each good you can buy will increase.
Technological progress since the Industrial Revolution has been accompanied by a dramatic rise in wages Consumer Equilibrium - the slope of the budget line is equal to the slope of the indifference curve
Real income the amount you can actually buy with your nominal income.
Depends on: (1) how much money you have (your budget or your income), (2) the price of product X and (3) the price of
product Y.
Y=product y • The Y intercept is 𝑀/ 𝑃𝑌 (total of Y if you spent all of your income on it)
Py= price of product Y • The slope is – 𝑃x/ 𝑃y
M= total income (we ignore the negative sign).
Get given R1 million
Notice that the feasibility frontier did not become steeper or flatter.
This is because
the wage rate did not change. The wage rate is equivalent to the
opportunity cost
- Py increase, Px unchanged of free time. In our scenario the wage rate is 15, so every hour spend
- Slope (MRT) becomes flatter during free
- Have to give up less Y for 1 unit of X time is a potential 15 lost.
- Opportunity cost of X falls (relatively cheaper) When the feasibility frontier makes a parallel shift you will ONLY see an
**double check income
effect. The income effect can be 0 or positive, but cannot be negative.
Meaning if
you get extra income, you will either work the same amount of hours or
LESS. If
you were to lose income, the opposite would be true. You would either
work the
ECO1010F Page 2
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