Lecture 3- Consumer Behaviour Flashcards
What is a utility function?
A way of assigning numbers to consumption bundles such that more preferred bundles get larger numbers than less preferred bundles. Mathematically: (x1,x2) > (y1,y2) if and only if u(x1,x2) > u(y1,y2)
What is a monotonic transformation and what is its key property?
A way of transforming one set of numbers into another while preserving their order. If U1 > U2, then f(U1) > f(U2). The slope of the graph is always positive
What is cardinal utility?
A theory that attaches significance to the magnitude of utility, where satisfaction can be measured quantitatively and expressed in numbers. The size of utility differences between bundles has operational significance
What is the Cobb-Douglas utility function?
U = x1^α * x2^β, where β and α are greater than zero. It’s the simplest algebraic expression that generates well-behaved preferences
What are the two common transformations of Cobb-Douglas function?
1) Natural log transformation: ln(U) = αln(x1) + βln(x2)
2) Power transformation: U^(1/(α+β)) = x1^(α/(α+β)) * x2^(β/(α+β))
How is marginal utility defined and calculated?
The rate of change in utility from consuming an additional unit of a commodity. For good 1: MU1 = ΔU/Δx1 = [U(x1 + Δx1,x2) - U(x1,x2)]/Δx1
What is the relationship between marginal utility and price at optimal consumption?
At optimal allocation, each good must yield the same marginal utility per currency spent: MU1/P1 = MU2/P2 = … = MUn/Pn
How is utility maximized subject to a budget constraint?
Using Lagrangian method: L = U(x1,x2) + λ(M - p1x1 - p2x2). First-order conditions: ∂U/∂x1 = λp1 and ∂U/∂x2 = λp2
What is λ (lambda) in utility maximization?
The marginal utility of income - it represents the additional utility gained from an extra unit of currency (e.g., one more naira)
What is the relationship between MRS and prices at consumer equilibrium?
At equilibrium, MRS equals the price ratio: MRS = p1/p2. This occurs at the point where the indifference curve is tangent to the budget line
How is MRS calculated using marginal utilities?
MRS can be calculated as the negative ratio of marginal utilities: MRS = -(MU1/MU2)
What are the two conditions for optimal consumer choice?
1) Spend all available income (budget constraint)
2) Choose bundle where MRS equals price ratio (tangency condition)
What happens to marginal utility if utility is multiplied by a scalar k?
If utility is multiplied by a scalar k, marginal utility will also be multiplied by the same scalar k
What does the point of tangency between indifference curve and budget line represent?
The optimal consumption bundle that maximizes utility while satisfying the budget constraint
How can you tell if a consumption bundle is optimal?
1) It must lie on the budget line (uses all income)
2) MRS must equal price ratio (tangency condition)
3) It must be on the highest attainable indifference curve
