Question

11. A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A^(1/3)B^(2/3). The price of goods A and B are $30 and $45, respectively. The consumer has a budget of $2700 that he can use to consume the two goods.

Question a) A new tax of 6% is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax?

Question b) Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B.

Answer 1

(i) When there is an imposition of per unit tax on Good B then as a result the consumption of good B decreases and also induces consumer to attain less utility, hence, this consumer is on the lower indifference curve, IC 2. In this case, there is a dual effect on the purchasing decision of the consumer. This per unit tax will lead to change both relative price that is known as substitution effect and purchasing power of the consumer that is known as income effect.

(i) When there is an imposition of a lump sum tax then as a result this will lead to reduce the income of the consumer which put the consumer on a lower indifference curve, IC 2. This lump sum tax will shift the budget line leftwards. In this case, the consumer’s purchasing decision is only affected by the income effect which reduces the purchasing power of the consumer.

We can conclude that the absence of substitution effect in case of lump sum tax induces the consumer to have more utility than under the per unit tax. Therefore, the consumer will prefer lump sum tax over a per unit tax.