Show all your working on this problem set.

1. (55 points) Ms Melendez has a utility function with regard to coffee: U = CE¹,

where Cis Columbian coffee and E is Ethiopian coffee. Initially use Y for her income

and pc and pe for the prices.

(a) (8 pts) How much of each type of coffee does Melendez consume (uncompensated

demand)?

(b) (4 pts) What is Melendez' indirect utility function?

(c) (8 pts) Work out her compensated demand functions for Columbian and Ethiopian

coffee.

(d) (3 pts) What are the numerical values for (a), (b) and (c) if her income is 20

pesos, and a bag of Columbian or Ethiopian beans costs 5 pesos.

(e) (4 pts) There is a drought in central Columbia and the price of a bag of Columbian

beans rises to 7 pesos. What income would Melendez need to reach her old utility

at the new prices?

onsume

(f) (4 pts) If she had this income, what quantities of each good would she cons

at the new prices?

(g) (4 pts) Given her actual income, what quantities of each good will she consume

at the new prices?

(h) (4 pts) What is the income effect of this price change for Ethiopian coffee?

(i) (4 pts) What is the substitution effect of this price change for Ethiopian coffee?

(i) (4 pts) Show that the Slutsky equation holds for this price change (using the

numbers you have already calculated for Ethiopian coffee).

(k) (8 pts) Calculate the change in Melendez' welfare caused by the price change,

using three different measures: both compensating variation (CV) and equivalent

variation (EV).