Question

A consumer uses his income I for the consumption of two goods ?₁ and ?₂. He maximises utility at given product prices ?₁, ?₂. His preferences with respect to both products can be described by an ordinal utility function ?(?_1,?₂), which exhibits a decreasing marginal rate of substitution (normal preferences). Please indicate whether the following statements are right or wrong in this context. If a statement is wrong, then describe briefly what is wrong (one sentence).

a) A double value of the ordinal utility function implies double satisfaction for the consumer.
b) At the utility maximum, the ratio of marginal utilities is equal to the ratio of product prices, i.e.

(??/??₁)/(??/??₂) = ?₁/ ?₂

c) In the case of a Cobb-Douglas utility function, the (Marshallian-) demand function for good ?₁ does not change when the price ?₂ changes.

d) The indirect utility function can be derived by substituting compensated demand functions for the consumption quantities into the utility function.

e) The value of the corresponding expenditure function depending on ?₁, ?₂ and the achieved maximum utility level is equal to the available income I.
f) The price induced quantity change described by the compensated (“Hicksian”) demand function is generally larger than the quantity change described by the Marshallian demand function, because the income effect is added to the substitution effect.
g) The Slutsky-equation shows that the income effect of a change of ?₁ on the demand for ?₁ can be significant, even if the income elasticity of demand for ?₁ is equal to zero.

Answer 1

second part- the statement will be true because the consumer will not substitute good x with good y any more he will be satisfied