Question

Suppose that a consumer has perfect complements, or Leontief, preferences over bundles of non-negative amounts of each of two commodities. The consumer’s consumption set is R^2(positive). The consumer’s preferences can be represented by a utility function of the form U(x1, x2) = min(x1, x2).

1. Illustrate the consumer’s weak preference set for an arbitrary (but fixed) utility level U.

2. Illustrate a representative iso-expenditure line for the consumer.

3. Illustrate the consumer’s utility-constrained expenditure minimisation problem.

4. Illustrate the derivation of the consumer’s compensated (or Hicksian) demand curve for commodity one.

5. Find the algebraic expression for the consumer’s compensated (or Hicksian) demand functions for commodity one and commodity two?

6. Find an algebraic expression for the consumer’s expenditure function.

Answer 1

The indifference curves will be L shaped as increasing consumption of any good without the other keeps the utility same. There will be kinks at the 45 degree line. The weak preference sets will be in the northeast direction of the curves, including the curve.

As there is no substitution effect the Hicksian and Marshallian demand functions will be the same. Optimum will be where both goods are equal. Using that, all required functions are derived