Study guide: Consumer Behavior for Transition

📋 Course Outline

1. Consumer Preferences
2. Indifference Curves
3. Utility and Marginal Substitution
4. Curvature and Types of Goods
5. Budget Constraint and Market Trade
6. Constrained Consumer Choice
7. The Consumer’s Optimization Problem
8. Cobb-Douglas Demand
9. Quasilinear and Special-Case Demand
10. Policy and Consumer Behavior

📖 1. Consumer Preferences

★ Must-know

• Consumer preferences rank bundles of goods according to the pleasure or satisfaction obtained from consuming them.

📌 Completeness requires a consumer to rank any two bundles as a ≻ b, b ≻ a, or a ∽ b.

📌 Transitivity requires that if a ≻ b and b ≻ c, then a ≻ c.

Further detail

📌 Strict preference is written a ≻ b, weak preference a ≿ b, and indifference a ∽ b.

📌 The more-is-better assumption says that, all else equal, more of a good is preferred to less, unlike the case of a bad.

📖 2. Indifference Curves

🔑 Key Concepts & Definitions

• Indifference curve: The set of all bundles that a consumer considers equally desirable and that provide the same utility.

★ Must-know

📌 Indifference curves cannot cross or be thick, and they slope downward under the assumptions presented.

Further detail

• An indifference curve passes through every possible bundle.

📌 With more-is-better preferences, bundles on indifference curves farther from the origin are preferred to bundles on curves closer to the origin.

📖 3. Utility and Marginal Substitution

🔑 Key Concepts & Definitions

• Utility: A numerical measure that represents the relative ranking of possible consumption bundles.
• Marginal utility: The additional utility from consuming one more unit of a good while holding consumption of other goods constant.
• Marginal rate of substitution: The maximum amount of one good a consumer will sacrifice to obtain one more unit of another good.

★ Must-know

📌 Utility is ordinal rather than cardinal: it ranks bundles but does not measure how much more one bundle is valued than another.

📐 Formula - The marginal rate of substitution is the slope of the indifference curve and is expressed as $MRS=\frac{dq_2}{dq_1}=-\frac{MU(q_1)}{MU(q_2)}$.

Further detail

• The utility function U(q1,q2) assigns utility measures to possible bundles of quantities q1 and q2.

📌 A positive monotonic transformation of a utility function preserves the preference ordering even if it changes the utility values.

📐 Formula - The marginal utility of good q1 is $MU(q_1)=\frac{\partial U}{\partial q_1}$.

📖 4. Curvature and Types of Goods

🔑 Key Concepts & Definitions

• Perfect substitutes: Goods between which a consumer is completely indifferent and that can be traded at a constant marginal rate of substitution.
• Perfect complements: Goods consumed in fixed proportions, such as apple pie and ice cream in the example.

★ Must-know

• For many typical indifference curves that are convex to the origin, the marginal rate of substitution diminishes along the curve.

Further detail

📐 Formula - For perfect substitutes with utility $U(C,P)=iC+jP$, where i and j are constants, the marginal rate of substitution is constant at i/j.

• The marginal rate of substitution for perfect complements is undefined.

• Cobb-Douglas indifference curves do not reach the axes, whereas quasilinear indifference curves reach one of the axes.

📐 Formula - A Cobb-Douglas utility function is $U(q_1,q_2)=q_1^\alpha q_2^{1-\alpha}$.

📐 Formula - A quasilinear utility function can be written as $U(q_1,q_2)=u(q_1)+q_2$.

💡 Memory Hook

Perfect substitutes allow constant-rate trade; perfect complements are consumed in fixed proportions.

📖 5. Budget Constraint and Market Trade

🔑 Key Concepts & Definitions

• Marginal rate of transformation: The market rate at which a consumer can trade one good for another and equals the slope of the budget line.

★ Must-know

📐 Formula - The budget constraint for two goods is $p_1q_1+p_2q_2=Y$.

Further detail

• If consumers cannot save or borrow, current-period income determines their budget.

📐 Formula - The budget line can be written as $q_2=\frac{Y}{p_2}-\frac{p_1}{p_2}q_1$.

📐 Formula - The marginal rate of transformation is $MRT=\frac{dq_2}{dq_1}=-\frac{p_1}{p_2}$.

• With p1 = 1€, p2 = 2€, and Y = 50€, the budget line is $q_2=25-\frac{q_1}{2}$.

📖 6. Constrained Consumer Choice

🔑 Key Concepts & Definitions

• Interior solution: The optimal bundle is at a tangency point between an indifference curve and the budget line, with both goods consumed in positive quantities.
• Corner solution: The optimal bundle is at a boundary and the indifference curve is not tangent to the budget line.

📝 Essential Points

• The optimal consumer bundle is on the highest attainable indifference curve given the budget constraint.

📐 Formula - At an interior optimum, $MRS=MRT$, or equivalently $\frac{MU(q_1)}{MU(q_2)}=\frac{p_1}{p_2}$.

💡 Memory Hook

An interior solution is tangent to the budget line; a corner solution is not.

📖 7. The Consumer’s Optimization Problem

★ Must-know

📐 Formula - The consumer chooses quantities to maximize utility subject to the budget constraint: $\max_{q_1,q_2} U(q_1,q_2)\quad\text{s.t.}\quad Y=p_1q_1+p_2q_2$.

• The optimal quantities q1* and q2* are functions of prices p1 and p2 and income Y.

Further detail

• The consumer's problem can be solved using substitution or the Lagrangian method.

📌 Under the more-is-better assumption, the consumer exhausts the budget at the optimum.

📖 8. Cobb-Douglas Demand

★ Must-know

📐 Formula - For Cobb-Douglas utility $U(q_1,q_2)=q_1^\alpha q_2^{1-\alpha}$, the optimal demands are $q_1=\frac{\alpha Y}{p_1}$ and $q_2=\frac{(1-\alpha)Y}{p_2}$.

• In the Cobb-Douglas demands, α is the share of income spent on good 1 and 1−α is the share spent on good 2.

Further detail

• Cobb-Douglas demand for good 1 does not depend on p2, and demand for good 2 does not depend on p1, so the goods are neither substitutes nor complements in this model.

• Both Cobb-Douglas quantities rise when income Y rises and fall when their respective own price rises, so both goods are normal goods.

• The Cobb-Douglas utility function represents a situation in which the share of income spent on each good is fixed.

📖 9. Quasilinear and Special-Case Demand

★ Must-know

📐 Formula - For quasilinear utility $U(q_1,q_2)=q_1-\frac{1}{2}q_1^2+q_2$, the interior demands are $q_1=\frac{p_2-p_1}{p_2}$ and $q_2=\frac{Y}{p_2}-\frac{p_1}{p_2}\frac{p_2-p_1}{p_2}$.

📌 For the stated quasilinear utility, if p1 ≥ p2 then the corner solution is q1=0 and q2=Y/p2; if p1 < p2 then the solution is interior with both quantities positive.

Further detail

• Quasilinear demand for good 1 does not depend on income, decreases with p1, and increases with p2.

• For an interior quasilinear solution, demand for good 2 increases with income, decreases with p2, increases with p1 when p1>p2/2, and decreases with p1 when p1<p2/2.

📐 Formula - With perfect substitutes and utility $U=q_1+q_2$, if p1<p2 the demands are q1=Y/p1 and q2=0, while if p1>p2 they are q1=0 and q2=Y/p2.

📐 Formula - With perfect complements and utility $U=\min\{q_1,q_2\}$, the consumer chooses q1=q2=q and the optimal quantity is $q=\frac{Y}{p_1+p_2}$.

• With perfect substitutes and equal prices p1=p2, the quantities of the two goods are undetermined by the stated solution.

• The substitution and Lagrangian methods used for ordinary interior solutions cannot be applied to the stated perfect-substitute and perfect-complement cases.

📖 10. Policy and Consumer Behavior

★ Must-know

• Public and private institutions can directly affect a good's price through taxes, subsidies, and price reductions.

📌 An indirect price effect on another good's demand depends on whether the goods are substitutes or complements.

Further detail

• The effect of a direct price change on demand for that good depends on its price elasticity.

• Public institutions can affect demand by changing income Y to increase or decrease it.