1. Problem associated with first video: Increasing transformation Consider the following utility function u(x1, x2) = x1x2.
(a) Calculate the MRS for this utility function.
(b) Compute and compare the MRS for the bundles (x1, x2) = (1, 2) and (x1, x2) = (2, 1). What does this comparison tell us about the preferences of the person with this utility function?
(c) Consider the bundles (x1, x2) = (4, 4) and (x1, x2) = (1, 9). Which bundle is the most preferred (i.e. yield the highest utility)?
(d) Consider the following function f(x) = âx and then define a new utility function v(x1, x2) = f (u(x1, x2)).
i. Show that v(x1, x2) is an increasing transformation of u(x1, x2).
ii. Answer, without calculating, which of the bundles in question c) above will be the
most preferred according to v(x1, x2).
iii. Calculate the MRS for v(x1,x2). How it compares with the MRS for u(x1,x2). Why?
1. Problem associated with first video: Increasing transformation Consider the following utility function u(x1, x2) = x1x2.
(a) Calculate the MRS for this utility function.
(b) Compute and compare the MRS for the bundles (x1, x2) = (1, 2) and (x1, x2) = (2, 1). What does this comparison tell us about the preferences of the person with this utility function?
(c) Consider the bundles (x1, x2) = (4, 4) and (x1, x2) = (1, 9). Which bundle is the most preferred (i.e. yield the highest utility)?
(d) Consider the following function f(x) = âx and then define a new utility function v(x1, x2) = f (u(x1, x2)).
i. Show that v(x1, x2) is an increasing transformation of u(x1, x2).
ii. Answer, without calculating, which of the bundles in question c) above will be the
most preferred according to v(x1, x2).
iii. Calculate the MRS for v(x1,x2). How it compares with the MRS for u(x1,x2). Why?
