Peter's utility from vacations (V) and restaurant meals (R) is given by the function

U(V, R) = V 2R.

The price of vacations is pV and the price of restaurant meals is

pR. in dollars per unit Peter has an income M in dollars.

i. Use the Lagrangean approach to find the relationship be- tween the quantity of R chosen by Peter as a function of prices and income. This relationship is called Demand func- tion for R. [10 marks]

ii. Calculate the area under the demand function for R when the price pR rises from 50 to 75, given pV = 200 and M = 1500. [5 marks]

iii. If p3 = 50, pV = 200 and M = 1500, what is the change in the utility if the income rises by 1? [5 marks]