Question

Randy and Esther consume only blueberries (x1) and raspberries (x2). Randy has utility function UR = xR1 (xR2 )2 and Esther has utility function UE = (xE1 )2xE2 . Randy is endowed with 5 blueberries and 5 raspberries and Esther is endowed with 10 blueberries and 10 raspberries. (a) Derive the equation of the contract curve, i.e., find xR2 (xR1 ).

Answer 1

To derive the equation of the contract curve, we need to find the values of xR2 in terms of xR1.

Step-by-step explanation:

To derive the equation of the contract curve, we need to find the values of xR2 in terms of xR1. Let's start by finding the utility functions of Randy and Esther:

Randy's utility function: UR = xR1(xR2)2
Esther's utility function: UE = (xE1)2xE2

We know that Randy is endowed with 5 blueberries and 5 raspberries, while Esther is endowed with 10 blueberries and 10 raspberries. Based on these endowments, we can set up the equations:

5 = xR1 + xE1
5 = xR2 + xE2

Solving these equations, we can express xR2 in terms of xR1:

xR2 = 5 - xE2