# Existence of a Walrasian Equilibrium I was wondering how to tackle part b of this question. I've already completed part a) using the usual method of equating the MRS (kink point for the second utility function) then looking at feasibility but part b is confusing me as to where to start.

Do i look at the assumptions of the existence of a Walrasian equilibrium such as the utility functions being strictly increasing, concave and continuous and if so what do I do with the information? If anyone could give me a starting point i'd appreciate that.

Thanks

So after solving a), you have the demand functions $$x_{11}(p)$$, $$x_{21}(p)$$, $$x_{12}(p)$$, $$x_{22}(p)$$, right?
An equilibrium exists if there is such a $$p$$ for which there is no excess demand or excess supply*. In this scenario, the supply is constant, given by the endowment thus you are looking for a price $$p$$ for which $$x_{11}(p) + x_{21}(p) = \omega_{11} + \omega_{21}$$ and $$x_{12}(p) + x_{22}(p) = \omega_{12} + \omega_{22}.$$ If you have calculated the demand functions correctly it is enough to use one of these market clearing equations to determine for which parameters $$a$$,$$b$$ the equation can hold, as the other equation follows from this one and the budget constraints.
*A special case is if $$p = 0$$, in which case excess supply is possible in equilibrum.