1.   

Sam's utility on good 'A' is presented as below. utility = () = A. However, good 'A' is composed of two parts, x and y in the fixed proportion of one unit of x and two units of y. Hence Sam's utility function can be rewritten as () = (,) = min(, 2). a) (5 points) Graph Sam's indifference curve in terms of x and y for various levels of utility. Show that, regardless of the prices of the two parts, Sam will never alter the way he consumes good 'A'. b) (10 points) Calculate the demand functions for x and y. c) (5 points) Using the results from part (b), what is Sam's indirect utility function? d) (5 points) Calculate Sam's expenditure function: for each level of utility, show spending as a function of and.