Topic 4: Consumer Behaviour

Condition for optimum bundle when there is an interior solution and the indifference curve is smooth:

MRS₂,₁ = -p1/p2
p1x1+p2x2 = m

What does the slope of the budget line measure?

The slope of the budget line measures the cost of having more of x1 in terms of the amount of x2 foregone

Define MRS₂,₁

The marginal rate of substitution MRS2,1 is the rate at which a consumer is willing to substitute good 2 for good 1 while holding utility constant, and is equal to the slope of the indifference curve, dx2/dx1, in absolute value.

MRS₂,₁ formula in terms of u

-u1/u2

Definition of Marshallian/Uncompensated demand curves

These tell us the optimal choices the consumer will make as a function of prices and income

Own-price elasticity of demand

Cross-price elasticity of demand

Income elasticity of demand

Normal good

Positive income elasticity

Inferior good

Negative income elasticity

Luxuries

Income elasticity greater than one

Necessities

Income elasticity between zero and one

Ordinary good

Negative own price elasticity

Giffen good

Positive own price elasticity

Slutsky Equation Formula

What are the conditions for well-behaved preferences?

Completeness: any two bundles can be compared

Reflexivity: a bundle is weakly preferred to itself

Transitivity

Continuity: if you prefer bundle A to bundle B, then any bundle that is very close to A will also be preferred to B

A utility function is a continuous function such that

X is weakly preferred to Y iff u(X)≥y(Y)

If the consumer sold all of their endowments they would generate an income of

Of the change from x1a to triangle x1 to x1b, which is substitution effect

Change from x1a to triangle x1

When the Slutsky equation’s consumer has an endowment of good 1(w1) how does the equation change?

Cross-price Slutsky equation

Compensated cross-price effects are … in the Slutsky equation

Symmetric

How to formalise Slutsky equation for labour hours