Colette and Hans both consume the same goods in a pure exchange economy. Colette is originally endowed with 15 units of good 1 and 12 units of good 2. Hans is originally endowed with 97 units of good 1 and 4 units of good 2. They both have the utility function U(x₁, x₂) = . If we let good 1 be the numeraire, so that p₁ = $1, then what will be the equilibrium price of good 2?

Question

Quizplus · Accepted Answer

In order to find the equilibrium price of good 2, we need to find the ratio of the marginal utilities of good 1 and good 2 for both Colette and Hans, and then set them equal to each other. 
For Colette: 
MU1/MU2 = (11S1U1B1S1U1B0)/(11S1U1B2S1U1B0)
MU1/MU2 = S1U1B1S1U1B0/S1U1B2S1U1B0 = 15/12 = 1.25
For Hans: 
MU1/MU2 = (11S1U1B1S1U1B0)/(11S1U1B2S1U1B0)
MU1/MU2 = S1U1B1S1U1B0/S1U1B2S1U1B0 = 97/4 ≈ 24.25
Setting the two ratios equal to each other: 
1.25 = 24.25pS1U1B11S1U1B0/pS1U1B21S1U1B0 
pS1U1B21S1U1B0 ≈ $14
Therefore, the equilibrium price of good 2 is approximately $14. Answer choice (A) is correct.

Colette and Hans Both Consume the Same Goods in a Pure