John a hedge fund CEO, has a monthly budget of $1,600 to buy whisky and cigars. A good bottle of whisky costs $50 while a

good box of cigars costs $100. John's preferences for whisky and cigars are represented by the utility function

U(w, c) = w^0.75c^0.25 (this is a Cobb-Douglas utility function), where w is measured in bottles and c in boxes.

a) In a diagram with w measured along the horizontal axis, draw John's budget constraint.

b) Write the expression of a John's indifference curves when his utility level is U = 2.

c) Find the expression of John's MRS of cigars for whisky at a generic whisky/cigar combination (w,c).

d) Using the Lagrangian method, find John's optimal combination of whisky and cigars.

e) In your diagram, add an indifference curve to illustrate John's optimal choice.

We are interested in the way price changes might affect John's purchases of whisky and cigars and so we wish to determine the

expression of John's demand.

f) Label the price of whisky Pw and keeping the price of cigars at $100 per box and John's budget at $1,600, find

John's demand for whisky (this will be a function Qw = D(Pw)).

g) Now use the letter Y to label John's income and the letters Pc to label the price of cigars and find John's demand

for whisky as a function of Pw, Y, and Pc.

h) Discuss your findings. How would an increase in income affect John's purchases of whisky? Does he consider

whisky a necessity, a luxury or neither? How would an increase in the price of cigars affect John's purchases of whisky?

Does he consider cigars a gross complement, a gross substitute or an unrelated good to whisky?