Question

Amanda consumes blue (good 1) and red (good 2) pencils. Initially, each of these goods costs 1 dollar but for some unknown reason, the price of blue pencils doubles to 2 dollars. Does the price increase make Amanda worse off when her preferences are described as (a) U = min{x1, 2x2}, (b) U = 3x1 + 2x2, or (c) U = x1 + x2? Argue carefully!

Answer 1

Answer: case1:

When utility function is

min u(x1, 2x2), She will always demand x1= 2x2 as both good are compliment of each other in this case. So, increase in price for good 1 doubles then budget curve will pivot l left has a result now she will consume less of both goods. Hence, she is worse off in this case.

Case2: When we have utility function

U(x1,x2) = 3x1+ 2x2

In this case she consumes only x1 intially as it gives more utility in compare to x2.

Now price of x1 gets double so it is better for her to switch her consumption to only good x2. She will be worse off in this case too.

Case3: in this case she will be neither worse off nor better off. She will simply switch her consumption for good 2 as each good has same weight in her utility function.