Chapter 7 Flashcards
Budget Line & Equation
- Shows all possible combination of two goods that a consumer is bale to purchase when spending of his or her income
- A bundle of goods which lies on the budget line is attainable, and such that the consumer spends all of his or her income
- A bundle of goods which lies above the budget line is not attainable
- M=Px(Qx)+Py(Qy)
where M=Money income of the consumer; Px= Price of good-X; Py=Price of good-Y Qx= Quantity of good -X; Qy= Quantity of good-Y
Shifts of the Budget Line
A change in the buyer’s income is associated with a parallel shift of the budget line.
⚫ The BL shifts outward when the buyer’s income increases.
⚫ The BL shifts inward when the buyer’s income decreases.
A change in the price of Good X (labelled on the horizontal axis) is associated with a
pivot shift of the budget line along the horizontal axis.
⚫ It shifts inward along the horizontal axis when the price of the Good X increases.
⚫ It shifts outward along the horizontal axis when the price of the Good X decreases.
A change in the price of Good Y (labelled on the vertical axis) is associated with a
pivot shift of the budget line along the vertical axis.
⚫ The BL shifts inward along the horizontal axis when the price of the Good Y increases.
⚫ The BL shifts outward along the horizontal axis when the price of the Good Y decreases
Total Utility VS Marginal Utility
- Measures the total satisfaction provided by the consumption of a given bundle of products
- Measures the satisfaction gained from the last unit of a product consumed.
THE LAW OF DIMINISHING MARGINAL UTILITY
- The MU decreases as the quantity consumed of a product by an individual increases.
Total & Marginal Utility Functions
Under the law of diminishing MU, the TU is concave.
- If preferences are monotonic, then the consumer can always increase his or her
satisfaction by increasing consumption.
- In that case, the MU is positive, and the TU is increasing.
- If preferences are non-monotonic, then the consumer can increase his or her satisfaction by increasing consumption up to a certain point only.
- Before that point, TU is increasing, and MU is positive.
- At that point, TU reaches a maximum, and MU is equal to zero.
- Beyond that point, TU is decreasing, and MU is negative.
- In this course, we will assume monotonic preferences.
MARGINAL UTILITY & INDIVIDUAL DEMAND CURVE
Assumption: Utility is measured in monetary terms (e.g. $ instead of utils).
- Under this assumption, the consumption of a good or service generates a
benefit whose value is equivalent to a certain amount of money. - For a given good or service, say Good X, the MUX curve is equal to the
individual demand curve for Good X.
MUX = DX
- Indeed, for any given price of Good X (PX), the consumer will purchase all units such that MUX ≥ PX (i.e. all units for which the benefit of consumption is greater than the cost of consumption).
Clearly, the consumer will not purchase the units such that MUX < PX (i.e. units for which the benefit of consumption is less than the cost of consumption).
- Therefore, due to the Law of diminishing MU, the last unit purchased is such that MUX = PX (i.e. the benefit of consumption is equal to the cost of consumption).
- It follows that the quantity demanded of Good X at price PX is equal to the inverse image (i.e. preimage) of PX under MUX.
- Finally, note that the Law of diminishing MU implies the MU curve is downward sloping and so the Law of Demand is satisfied.
INDIFFERENCE CURVES & It’s Properties
- A curve showing all possible combinations of 2 goods between which a consumer is indifferent (i.e. all possible combinations that provide the same level of TU).
Properties:
⚫ IC further from the origin represent higher levels of total utility.
⚫ If consumer preferences are monotonic, then the IC are decreasing.
⚫ Under the law of diminishing MU, the IC are convex.
⚫ Transitivity implies that IC can never intersect one another.
TO SUBSTITUTE (Indifference curves & Perfect Substitutes)
Question: If you substitute Good X for Good Y, do you get more of Good X and less of Good Y, or do you get more of Good Y and less of Good X?
- Answer: You get more of Good X and less of Good Y.
- Mnemonics: Substitute X for Y = X replaces Y.
- Example: If you initially have 5 rabbits and 40 berries and if you substitute 1 rabbit for 20 berries then you end up with 6 rabbits and 20 berries.
THE MARGINAL RATE OF SUBSTITUTION
- The Marginal Rate of Substitution (MRS) of Good X for Good Y measures the number of units of Good Y that must be given up in exchange for 1 additional unit of Good X, while keeping the same level of TU
- The negative sign is usually added for convenience, so the MRS is positive.
- The MRS is a psychological exchange rate specific to each consumer
MRS and Indifference Curves
The MRS of Good X for Good Y measures the absolute value of the gradient of the indifference curves in the (x, y) plane.
- Under the law of diminishing MU, indifference curves are convex, and so the MRS is decreasing.
- If Good X and Good Y are perfect substitutes, then indifference curves are linear, and have a slope of -1, so the MRS is constant and equal to 1
Consumer Choice
- The best combination of Good X and Good Y is such that the consumer spends all his or her income.
- It follows that the best combination of Good X and Good Y lies on the BL.
- However, there are many combinations of Good X and Good Y that lie on the BL, so we need a second condition to determine which one is the best.
Consumer Choice with Equation (Good X)
- Consider a combination of Good X and Good Y that lies on the BL.
What happens when the consumer gives up 1 unit of Good X?
On the one hand, he or she loses MUX utils of TU.
On the other hand, the consumer now has $PX left, that can be used to purchase PX / PY additional units of Good Y.
As a result, he or she gains MUY xPX / PY utils of TU.
Overall, giving up 1 unit of Good X is beneficial as long as:
- MUX < MUY x PX / PY ⇔ MUX / MUY < PX / PY ⇔ MRSXY < PX / PY
Consumer with Equation (Good Y)
Consider a combination of Good X and Good Y that lies on the BL.
What happens when the consumer gives up 1 unit of Good Y?
On the one hand, he or she loses MUY utils of TU.
On the other hand, the consumer now has $PY left, that can be used to purchase PY / PX additional units of Good X.
As a result, he or she gains MUX xPY / PX utils of TU.
Overall, giving up 1 unit of Good Y is beneficial as long as:
MUY < MUX x PY / PX ⇔ MUX / MUY > PX / PY ⇔ MRSXY > PX / PY
THE EQUI-MARGINAL PRINCIPLE
If the MU per dollar spent on Good X is greater than the MU per dollar spent on Good Y (i.e. MUX / PX > MUY / PY ), then the consumer should buy more of Good X and less of Good Y (i.e. it should substitute Good X for Good Y).
As a result, due to the law of diminishing MU, the MU per dollar spent on Good X will decrease whereas the MU per dollar spent on Good Y will increase until the EMP is satisfied.
If the MU per dollar spent on Good X is smaller than the MU per dollar spent on Good Y (i.e. MUX / PX < MUY / PY ), then the consumer should buy less of Good X and more of Good Y (i.e. it should substitute Good Y for Good X).
As a result, due to the law of diminishing MU, the MU per dollar spent on Good X will increase whereas the MU per dollar spent on Good Y will decrease until the EMP is satisfied.
CONSUMER EQUILIBRIUM
The best combination of Good X and Good Y is such that:
⚫ The consumer spends all his or her income.
⚫ The MRS is equal to the price ratio.
Wasi Haider Shah – A levels
