Suppose the only two goods you care about in the world are French wine (x) and Cuban cigars (y) and your utility function is given by u(x,y)=xy. You have no income, and the only thing in the world you possess is a large box you have just inherited from your rich uncle who passed away last week (of liver and lung cancer.) You open the box, and much to your liking, you find it contains 9 bottles of fine French wine and 3 boxes of exquisite Cuban cigars. Currently, the wine sells for $1 per bottle, and the cigars sell for $9 per box. Just as you receive the inheritance, you read the headline: "President Lifts Embargo - Price of Cuban Cigars Falls to $4 per Box!"
a. Determine the income (or wealth) and substitution effects of a decrease of the price of cigars from 9 to 4. (Assume
fractions of bottles and cigars can be bought.)
b. Are cigars a normal or inferior good for you?
c. How much would you have been willing to pay the President in order not to lift the embargo?
What will be an ideal response?
. Income in our case is based on the value of the endowment -- which is 36 before the price change and 21 afterwards. Thus, to total change in the consumption bundle is from an initial (18,2) to a final 
.To isolate the substitution effect, we need to start by finding the utility level before the price change --- which is 18(2)=36. We then solve
to get the bundle (12,3).
The substitution effect therefore takes us from (18,2) to (12,3) while the wealth effect takes us from (12,3) to (11.5, 2.625).
b. Cigars are normal goods. It may appear like the income effect is negative, but that's because the budget is endogenous -- Cobb-Douglas tastes are always over normal goods.
c. If embargo is lifted, utility will be (11.5)(2.625)=30.1875. If prices remained at the pre-embargo levels and you had just enough income E to reach this utility level, it would have to be that 
(because you would be consuming according to the demand functions in (a) with the price of wine at 1 and the price of cigars at 9). Solving this equation, we get 
--- while the initial value of your endowment is 36. Thus, you would be willing to pay approximately $3 to avoid the lifting of the embargo.
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