# Problem i. The consumer side analogue to firm’s goal of profit maximization is the goal of utility maximization subject to a budget constraint.

1.     Problem

i.           The consumer side analogue to firm’s goal of profit maximization is the goal of utility maximization subject to a budget constraint. Utility means satisfaction. So let’s consider an individual who consumes only two goods: ale and bread. The quantity of ale is given in pints/week and the quantity of bread is given in loaves per week. Suppose the price of ale is \$2/pint and the price of a loaf of bread is .50/load.

Let Income \$8. The consumer’s utility is given below.

Let

0                        0                                         0                     0

1                      40                                         1                     15

2                      70                                         2                     23

3                      90                                         3                     30

4                     100                                         4                     35

5                     105                                         5                     38

6                     107                                         6                     40.5

7                     108                                        7                     42

8                     108.5                                      8                     43

a.   Which (Ale, Bread) bundle maximizes this consumer’s utility given the

budget constraint

b. Does this bundle violate our “bang for the buck” rule for maximization?

Explain.

Special Utility Functions

Compute U for the following functions and bundle.

i.           U ( ) =

(4, 0)

(3, 1)

(2, 2)

(1, 3)

(0, 4)