Lesson 2 - consumer theory

Question 1

Utlity - measure of satisfaction. Units are “utils.”

Answer 1

Property 1: Preferences must be representable by a utility function (completeness and transitivity assumed).
Property 2 (Typical): More is better (non-satiation); ∂U/∂x > 0 for “goods”.
Property 3 (Typical): Diminishing marginal utility (DMU); U(x) curve flattens as consumption rises.

Question 2

Marginal Utility (MU):

Answer 2

Additional utility from consuming one more unit of a good (MUx = ∂U/∂x). = (dU/dX)
Slope of the 𝑈(x) curve
* DMU says that the more you consume a good, the less impact each unit of the good has on your happiness

Question 3

Indifference Curves (ICs)

Answer 3

Show bundles providing equal utility. A consumer is indifferent between bundles on the same IC.

Indifference Map: A set of ICs showing different utility levels.

Typical IC characteristics:
Slopes downwards,
never cross,
convex to the origin. (if a preference has all 3 properties then its called a typical IC curve)

Question 4

Marginal Rate of Substitution (MRS)

Answer 4

Maximum units of one good a consumer will give up for one more unit of another good (MRS_FC = -dC/dF = MUF/MUC).

• negative of the slope of IC
  Note- MRS_Fc is positive (for typical preferences)

Diminishing MRS: ICs are convex; as consumption of one good increases, willingness to trade it decreases.

Question 5

Non-Typical Preferences:

Answer 5

Perfect Substitutes: Linear ICs; U(x, y) = ax + by. (the 2 goods are very similiar)

Perfect Complements: L-shaped ICs; U(x, y) = min{ax, by}.
(need both goods together to provide satisfaction)

Question 6

Budget constraint

Answer 6

Shows all affordable bundles given income (I) and prices (PF, PC).

Equation: PFF + PCC = I. (price*qty)

Relative Price: -PF/PC; (negative of the relative price of F and C)
the slope of the budget line - Negative of budget line slope is sometimes called the marginal rate of transformation

Changes in Budget Line:
Income change: Parallel shift.
Price change: Rotation around the intercept of the unchanged good.

Question 7

Optimal Choice:

Answer 7

The consumer’s goal is to maximize their utility (satisfaction) given their budget constraint.
Optimal Bundle: The point where the highest indifference curve touches the budget line. For typical preferences, this is a tangency point.

Question 8

Tangency Condition

Answer 8

MRS = relative price
(MUF/MUC = PF/PC).
At the optimal bundle (for typical preferences), the slope of the indifference curve (which represents the marginal rate of substitution, MRS) equals the slope of the budget line (which represents the negative of the relative price).

Subjective value equals objective value. -> subjective rate at which the consumer is willing to trade good F for good C (MRS) is equal to the objective rate at which the market allows them to trade (relative price).

Question 9

corner solution

Answer 9

A situation where the optimal bundle lies on one of the axes—meaning the consumer consumes zero units of one of the goods. This occurs when the MRS is either strictly greater than or strictly less than the relative price at the point where the indifference curve intersects the axis. The consumer would gain more utility by shifting their entire budget to one of the goods. There is no tangency point; the indifference curve intersects one of the axes.

Question 10

Algorithm for Optimal Bundle:

Answer 10

1. Derive Marginal Utilities (MUs):
   Find the partial derivative of the utility function with respect to each good. This gives the marginal utility of each good (MUx, MUy).
2. Derive Marginal Rate of Substitution (MRS):
   Calculate the MRS as the ratio of marginal utilities: MRSxy = MUx/MUy.
3. Apply the Tangency Condition:

Set the MRS equal to the relative price of the goods: MRSxy = Px/Py.
one equation.

4. Use the Budget Constraint:
   Write the budget constraint equation: Pxx + Pyy = I (where I is income). This creates a second equation.
5. Solve the System of Equations:
   Solve the two equations (from steps 3 and 4) simultaneously for the optimal quantities of goods x and y (x* and y*).

Corner Solutions: If the solution from step 5 results in a quantity of zero for one good, it indicates a corner solution. Re-evaluate by checking if the MRS is consistently greater than or less than the price ratio.

Non-Typical Preferences: For non-typical preferences (e.g., perfect complements), the tangency condition might not apply, and a different approach may be needed (like considering the kink points in L-shaped indifference curves for perfect complements).

Question 11

Demand

Answer 11

Individual Demand: Relationship between price and quantity demanded by a single consumer. Derived from optimal choice at various prices. Typically slopes downwards.
Market Demand: Sum of all individual demands at each price. Derived by horizontally summing individual demand curves.