In: Economics
Peta and Dudley live in a
two-person, two-commodity world. Quantities of the first good are
denoted by x while quantities of the second commodity are
denoted by y. Peta’s preferences can be represented by the
utility function uP(x,y)
= x y and Dudley’s are represented by the utility function
uD(x,y)
= min{x,y}. Peta is initially endowed with 3 units of commodity
1 and 4 units of commodity 2 while Dudley is initially endowed with
7 units of commodity 1 and 6 units of commodity 2.
(e) is not correct as you may find that they are not consuming 5 units of each goods at the equilibrium (see details). Hence, this option is not true.
(d) The prices of both goods are same as derived. Hence, this option is not true.
(c) This option is also not true as Dudley does not consume 6 units of each goods at the equilibrium.
(b) At a competitive equilibrium, Dudley must consume equal amounts of both goods, so the price of good 1 must equal the price of good 2. This statement seems to be true.
Find the detailed derivation below.