The focus of consumer theory is on the optimal choice of goods and services by individuals to maximize their utility.
A consumer wants to get the most utility possible given her budget constraint.
All possible bundles of goods she can consume given her disposable income/resources and market prices of goods
We are particularly interested in when the price of the good changes.
The demand curve for food slopes downwards for typical preferences.
The additional utility one receives from one additional unit of consumption of a good.
β ππ πΉπΉ ππ πΆπΆ
It states that the more you consume a good, the less impact each unit of the good has on your happiness.
Utility function, indifference curves, and budget line.
MRS FC = - dC/dF = MU_F / MU_C
ICs are convex to origin, meaning as the consumer consumes more F, she is less and less willing to give up consumption of C
As more consumers enter, market demand shifts right.
The goal of the Optimal Choice for a consumer is to maximize their total utility given their budget constraint.
On the budget line and on the highest (most NE) indifference curve.
When the optimal bundle is such that the quantity of one good is zero.
A review of basic math needed today
A bundle with utility level of 3
The utility level of 3 is preferred to the utility level of 2
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Understanding how economists model the consumer.
Utility increases in the NE direction, ICs slope downwards, ICs never cross one another, ICs are convex to the origin (bowed inwards)
When the slope of the indifference curve is greater than the slope of the budget line in absolute value, it means the consumer should consume more of good F and less of good C.
Market demand is the sum of individual consumersβ demand at any given price (sum horizontally in graphs).
Utility Functions represent the preferences of consumers and how they make choices based on maximizing their utility.
Individual Demand refers to the quantity of a good or service that an individual consumer is willing and able to purchase at a given price, holding all other factors constant.
Tastes/preferences and budget constraint
We are interested in how the individualβs demand for a good changes when conditions change.
MU_F / p_F >= MU_C / p_C
The concept of individual demand stems from the consumerβs optimal choice.
MU = dU / dx, where U is the utility and x is the quantity of the good.
The budget line shifts outward in a parallel manner
The tangency condition states that the ratio of the marginal utility of good F to its price should be equal to the ratio of the marginal utility of good C to its price.
ππ π₯π₯ , π¦π¦ = min ππ π₯π₯ , ππ π¦π¦
Use the tangency condition to get one equation in x and y, or use the ratio of the partial derivatives of the utility function to the prices of x and y.
The focus of Managerial Economics is on applying economic theory and methods to solve business problems.
The Marginal Rate of Substitution (MRS) is the rate at which a consumer is willing to give up some amount of one good in exchange for another while maintaining the same level of satisfaction.
The budget line changes
A consumer's choice can be characterized mathematically, or using indifference curves and the budget line.
The consumer's demand curve for food represents the combinations of food price and quantity that the consumer is willing to purchase, holding constant income, the price of clothing, and preferences.
Utils
The slope of the budget line is the negative of the relative price.
The subjective relative value equals the objective relative price.
Linear ICs
The consumer has the same level of utility from each bundle
The consumer is in equilibrium when the price-adjusted marginal utility of good F is equal to the price-adjusted marginal utility of good C.
Derive MRS using the partial derivatives of the utility function with respect to x and y.
Q = q_A + q_B + q_C = 30 - 2.5p if p β€ 10, Q = 20 - 1.5p if 10 < p β€ 12, Q = 14 - p if 12 < p β€ 14, Q = 0 if p > 14.
The focus of individual demand in consumer theory is on the behavior and preferences of a single consumer in the market.
Indifference curves
A function associates each element of a set to exactly one element of another set.
The arguments of the function are the elements being plugged into the function.
ππ(π₯π₯, π¦π¦, π§π§) = π₯π₯ β π¦π¦ + π§π§
marginal rate of transformation
ππ π₯π₯ , π¦π¦ = ππ π₯π₯ + ππ π¦π¦
Bundle D (100, 500)
Understanding how to derive market demand from individual demand.
q_B = 10 - p if p β€ 100, q_B = 0 if p > 100.
Find the optimal bundle again at different prices
The transition from consumer choice to demand involves individual demand and market demand.
A bundle with utility level of 2
Consumer wants to buy more of one good and less of another, but cannot due to negative quantities or prices.
Completeness and transitivity
Changes in income and changes in price
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The (maximum) number of units of good C that a consumer is willing to give up in order to obtain one more unit of good F
Individual demand is derived from preferences and the budget constraint.
The optimal bundle must lie on the budget line, so the budget line itself gives the second equation in x and y.
Consumer Theory is the study of how people decide to spend their money based on their preferences and budget constraints.
The aggregate demand for a good or service in the entire market.
Preferences
Consumer theory encompasses preferences, utility, and indifference curves, as well as the budget constraint and optimal choice.
The limit on the consumption bundles that a consumer can afford given their income and the prices of goods and services.
The budget constraint equation for the consumer's choice
A measure of satisfaction ('utility') from a good or bundle of goods
Partial derivatives
The slope of the indifference curve is the negative of the marginal rate of substitution (MRS).
We write βf/βx, βf/βy, or βf/βz to indicate the derivative with respect to x, y, or z respectively
πΆπΆ = β ππ πΉπΉ ππ πΆπΆ πΉπΉ + πΌπΌ ππ πΆπΆ
We treat y and z as if they were constant
An IC represents the set of bundles that give a consumer an identical utility level
A consumer is indifferent for all bundles found on the same IC
More is always better, even if just a little bit better. Mathematically, it is represented by an increasing function: β^2U/βx^2 > 0. This applies to 'goods' only; a 'bad' (e.g. pollution) should be decreasing, i.e. β^2U/βx^2 < 0.
It indicates that the increment is getting smaller as consumption of a good rises, represented by the function becoming flatter: U(x) becomes flatter as consumption of x rises.
The budget line rotates about one intercept
Be careful about which intercept and which price is being affected
The conditions for optimal choice are understood and used.
The subjective relative value of F and C from the perspective of the individual consumer
When the slope of the indifference curve is less than the slope of the budget line in absolute value, it means the consumer should consume less of good F and more of good C.
Solve the 2 equations in 2 unknowns to get the optimal values of x and y.
q_C = 14 - p if p β€ 140, q_C = 0 if p > 140.
The Budget Constraint represents the combinations of goods and services that a consumer can afford given their income and the prices of the goods.
Marginal Utility is the additional satisfaction or benefit that a consumer derives from consuming an additional unit of a good or service.
Market Demand refers to the total quantity of a good or service that all consumers in a market are willing and able to purchase at a given price, holding all other factors constant.
Consumer Theory
Bundle D (5πΉπΉ, 5πΆπΆ)
Bundle E (15πΉπΉ, 15πΆπΆ)
food (F) and clothing (C)
Goods F and C together forming a 'bundle'
A set of ICs representing different utilities of a consumer
L-shaped ICs
Derive MUs using the partial derivative of the utility function with respect to x and y.
q_A = 6 - 0.5p if p β€ 120, q_A = 0 if p > 120.
Indifference Curves represent combinations of goods that give the consumer equal satisfaction and are used to analyze consumer preferences.
