Question 1 (24 points)

Let a consumer's utility be given by U (x, y, z) = In(x) + In(y) + In(2 + z). The

consumer has a budget constraint of x + 3y + 2z = 18.

1. What are the optimal choices for this consumer? (7 marks)
2. What would the optimal choices be if income were increased from 18 to 19? Compute the optimal bundle that maximises the utility function and show the changes in the optimal bundle from a) to b) in a graph. (7 marks)
3. What is the consumer's utility in each case? (4 marks)