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Consumer Theory

Utility-Maximization Model

Constrained optimization: Marginal Benefit = Marginal Cost 1. Objective: Maximize utility 2. Satisfy budget constraints

Utility

Indifference Curves

At any point on the curve, the combination of the two will leave the consumer equally well off or equally satisfied—hence indifferent.

Shows all combinations of __ that provide the same utility Slope gives
Goods-Indifference Curve two commodities at the same time point MRS
Fisher’s Time-Indifference Curve same commodity at different time points time_indifference_curve

Properties

Property Satisfies Assumption
Higher indifference curve is preferred non-satiation
Indifference curves are downward-sloping non-satiation
Indifference curves never intersect transitivity
Only one indifference curve through every combination completeness
Convex to the origin Diminishing marginal utility & MRS

Utility

Utility is ordinal; not nominal: can only rank

Let \(Q\) be consumption

\[ U \propto Q \]

Marginal Utility

Derivative of utility function

\[ \begin{aligned} \dfrac{dU}{dQ} &\propto \dfrac{1}{Q} \\ \dfrac{dU}{dQ} &> 0 \end{aligned} \]

Diminishing Marginal Utility

With increased consumption - total utility increases - marginal utility decreases

This is why price of a good does not increase proportionately with the quantity. eg: Milk

MRS

Marginal Rate Substitute

Rate at which you are willing to substitute one good for another

\[ \begin{aligned} \text{MRS} &= \dfrac{dQ_2}{dQ_1} \\ &= -\dfrac{\text{MU}_1}{\text{MU}_2} \end{aligned} \]

Diminishing MRS

With increased consumption, MRS decreases

Budget

Expenditure

\[ y = \sum_i P_i Q_i \]

where - \(y =\) spent amount - \(P_i =\) price of commodity \(i\) - \(Q_i =\) quantity of commodity \(i\)

Budget Line

Opportunity Set

Set of choices available to you given the constraints

MRT

Marginal Rate of Transformation = Slope

Shows the real/opportunity cost of \(x\) (how much we're sacrificing \(y\))

MRT of producing/consuming \(x\) wrt \(y\) shows no of units of \(y\) to be sacrificed to increase the output/consumption of \(x\) by one unit

\[ \begin{aligned} y &= f(x) \\ \text{MRT}_{x,y} &= -\frac{\mathrm{d} y}{\mathrm{d} x} \end{aligned} \]

Changes

Change Outcome Example
Cost Change in Slope Increase in price of pizza
Budget Change in intercept Decrease in income
## Choice

Highest indifference curve achievable given the budget: the tangency

Point at which MRT = MRS

Rate at which you want = Rate at which market will allow

Case Study

Cash Transfer vs Food Stamps

Cash Transfer Food Stamps
Belief Everyone is responsible and makes the right choices Paternalism: Economist knows better than the person
Limitation May lead to black market
Last Updated: 2024-12-26 ; Contributors: AhmedThahir, web-flow

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