Sometimes we can infer something about tastes from observing only two choices under two different economic circumstances.
A. Suppose we consume only beer and pizza (sold at prices p1 and p2 respectively) with an exogenously set income I.
(a) With the number of beers on the horizontal axis and the number of pizzas on the vertical, illustrate a budget constraint (clearly labeling intercepts and the slope) and some initial optimal (interior) bundle A.
(b)When your income goes up, I notice that you consume more beer and the same amount of pizza. Can you tell whether my tastes might be homothetic? Can you tell whether they might be quasilinear in either pizza or beer?
(c) How would your answers change if I had observed you decreasing your beer consumption when income goes up?
(d) How would your answers change if both beer and pizza consumption increased by the same proportion as income?
B. Suppose your tastes over beer (x1) and pizza (x2) can be summarize by the utility function u(x1,x2)= x21 x2 and that p1=2, p2=10 and weekly income I=180.