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ECN6510

Microeconomic Analysis

Workshop 1: Consumer Theory

This workshop will require you to carefully consider the axioms of consumer preferences, apply the Lagrangian and consider duality in the context of consumer theory.

The workshop will develop a range of transferable skills including: critical evaluation, problem solving and mathematical skills.  

1. How realistic do you think the axioms of consumer choice are? How do lexicographic preferences fit into this approach?

2. With reference to the Marshallian demand functions derived from the Cobb-Douglas utility function, explain the properties of these demand functions.

3. Assume that the individual has a utility function given by :

(i) Derive the Marshallian demand functions for good x and good y.

(ii) Comment on the demand for good x. What are the income effects for good x?

4. Under what conditions will Hicksian and Marshallian demand functions coincide?

5. Outline one area of microeconomics where indirect utility functions are particularly useful.

6. A consumer buys x and y in the fixed proportions 1x with 2y.

(i) What do the individual’s indifference curves look like?

(ii) Derive the Marshallian demands for x and y (without using the Lagrangian technique).

(iii) Use Slutsky’s equation to evaluate the own and cross price substitution effects.

7. Attempt Question 4 Part (B) of the past paper questions (also shown below).

The minimum cost of achieving target utility  is given by

(i) Calculate the effect on the demand for good  of an increase in its own price () assuming the consumer’s objective is the attainment of target utility  .

Hint: Use Shepherd’s Lemma: .  Where m* is the expenditure function.

(ii) Rationalise the direction of the response in (i).