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7.4 The agents in a two-commodity exchange economy have utility functions
Ua(xa) log(xa) + 2 log(xa)
l 2
Ub(xb) 2 log(xb ) + log(xb )
l 2
i
where xh is the consumption by agent h of good i, h a, b; i 1, 2. The property distribution is given by the endowments Ra (9, 3) and Rb (12, 6).
1. Obtain the excess demand function for each good and verify that Walras' Law is true.
2. Find the equilibrium price ratio.
3. What is the equilibrium allocation?
4. Given that total resources available remain fixed at R Ra+ Rb (21, 9), derive the contract curve.
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