MEF121 Advanced Microeconomics Assignment

Assignment Help Microeconomics

Reference no: EM132493802

MEF121 Advanced Microeconomics - ZCAS University

SECTION A QUESTION 1.

Suppose we have two goods, whose quantities are denoted by A and B , each being a real number. A consumer's consumption set consists of all (A; B ) such that A ≥ 0 and B > 4. His utility function is:
U (A, B) = ln(A + 5) + ln(B - 4).
The price of A is p and that of B is q; total income is I. You have to find the consumer's demand functions and examine their properties. You need not worry about second-order conditions for now.

(i) Solve the problem by Lagrange's method, ignoring the constraints A ≥ 0, B > 4. Show that the solutions for A and B that you obtain are valid demand functions if and only if I ≥ 5p + 4q.

(ii) Suppose I ≥ 5p + 4q. Solve the utility maximization problem subject to the budget constraint and an additional constraint A ≥ 0, using Kuhn-Tucker theory (Bear in mind that the Kuhn-Tucker conditions coincide with the ordinary first-order Lagrangian conditions). Show that the solutions for A and B you get here are valid demand functions if and only if 4q < I ≤ 5p + 4q. What happens if I ≤ 4q?
In each of the following parts, consider the above cases (i) and (ii) separately.

(iii) Find the algebraic expressions for the income elasticities of demand for A; B. Which, if either, of the goods is a luxury?

(iv) Find the marginal tendencies to spend on the two goods. Which, if either, of the goods is inferior?

(v) Find the algebraic expressions for the own price derivatives ∂A/∂p, ∂B/∂q. Which, if either, of the goods is a Giffen good?

SECTION B QUESTION 2.

(i) A preference relation >_~ on X is supposed to be rational. Show the following.
(a) Reflexive: For any x ∈ X, x ~ x.
(b) Transitive: For any x; y; z ∈ X, if x > y and y > z, then x > z.
where ~ and > are defined as follows:
a ~ b <=> a >_~ b and b >_~ a a > b <=> a >_~ b and b >_~ a

(ii) Examine Galina, Karina and Lara and the relation at least as tall as. As in Galina is at least as tall as Karina. State whether this relation satisfies the completeness and transitivity properties? Taking the same group of individuals as above consider the relation strictly taller than and explain whether or not it is complete? Is the relation also transitive?

Attachment:- Advanced Microeconomics assignment.rar

Reference no: EM132493802

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