Question

The consumer’s utility function is U(a,b) = ab2, where a denotes the quantity of good A that the consumer consumes and b denotes the quantity of good B that the consumer consumes. The price per unit of good A is 4 Euros and the price per unit of good B is 8 Euros. Consumer’s income is 120 Euros.

a) Find the marginal utility of good A and the marginal utility of good B

b) Find the optimal quantity of good A and good B, for this consume

c) Government is considering 2 alternative taxation schemes:

- alternative 1: a tax of 12 Euros per unit of good A

- alternative 2: a tax of 8 Euros per unit of good B

If the consumer has to choose one of the taxation schemes, then which of these taxation schemes will the consumer choose? Provide calculations for proof.

Answer 1

a. The given utility function is:

Marginal utility of a is computed by differentiating the utility function with respect to a:

Similarly, marginal utility of b is:

b. The consumer's problem is:

At equilibrium, marginal rate of substitution is equal to the price ratio:

Substituting this value into the consumer's budget constraint:

c. Under alternative one, the consumer's new problem is:

Substituting the value of b derived in the previous part into the consumer's budget constraint:

Utility derived by the consumer after consuming this bundle is:

Under alternative two, the consumer's new problem is:

Substituting the value of b derived in the previous part into the consumer's budget constraint:

Utility derived by the consumer after consuming this bundle is:

Since the consumer derives a higher utility under alternative two, he would choose alternative two out of the given two taxation alternatives.