Title: Microeconomics / Q1 / lecture5

Q: utility maximization problem (UMP)
A: The consumer’s “problem” (goal) is to choose the “best”
consumption bundle(s) given prices p >> 0 and w > 0.

Q: The Walrasian Demand Correspondence/Function
A: The first figure has a unique solution, so it is a demand
function (note that preferences are strictly convex, so the
utility function is strictly quasiconcave). The second
figure has many solutions, so it is a demand
correspondence (and the preferences that produce it are
convex, but not strictly convex).

Q: Kuhn-Tucker (necessary) conditions
A: emonstrate that if
x* x(p, w) is a solution to the UMP, then a Lagrange
multiplier λ ≥ 0 exists such that, for all ℓ = 1, 2, ... L:

Q: marginal rate of substitution
A: Intuitively, it shows the relative “value” of the two goods
in terms of their contribution to the consumer’s utility. It
also shows how much good k the consumer requires to be
compensated for the decrease in utility from giving up 1
unit of good ℓ. The slope of the indifference curve in the
left figure below at the utility maximizing point is –MRS.

Q: Lagrange multiplier
A: It is the marginal (shadow) value of relaxing
the wealth constraint, which means that it is the marginal
utility of an increase in w (for the optimal bundle of x).