4. MRS and Consumer Choice

A consumer has preferences for avocados (a) and blueberries (b) which can be represented by the following utility function: U(a, b) = 20a 1 4 b 3 4 7

The price of avocados (pa) is $5 per unit while the price of blueberries (pb) is $9 per unit, and the consumer has income of $60.

1. Calculate the marginal rate of substitution of avocados for blueberries, MRS(a, b). What is the value of the MRS(a, b) for this consumer if she has: (A) two units of avocados (a = 2) and six units of blueberries (b = 6). (B) two unit of avocados (a = 2) and twelve units of blueberries (b = 12).

2. Given the price for avocados and the price for blueberries, is this consumer consuming the optimal ratio of avocados and blueberries in (A) and/or (B)? Would you tell the consumer to increase the ratio of avocados to blueberries, stay with the current bundle, or decrease the ratio of avocados to blueberries in each of these cases?

3. Write down the consumer's budget constraint.

4. Find the bundle of avocados and blueberries that maximizes the consumer's utility.