1. ## Competitive equilibirum

Consider the following scenario?

2 consumers - 1 & 2
2 commodities - bicycles(b) and wheat(w)
Same utility function - u(b,w) = bw
production functions -

b = sqrt(l_b) and w = 0.5*sqrt(l_w)

consumer 1 owns both the firms and consumer 2 owns 200 units of labour.

How do we find the competitive equilibirum for such a problem since there is not price term in the budget constraint/PPF?

2. ## Re: Competitive equilibirum

Hey kartik199.

I'm not an economics major and I haven't studied this stuff but from a mathematics point of view if you don't have enough information you either get it or assume it.

I'm looking (quite briefly) at the wiki site and I'm seeing other constraints that allow you to remove the prices.

If you are going to get help from non-economics majors in this forum you are going to have to give the sort of context that we lack with regards to economics (as opposed to mathematics).

3. ## Re: Competitive equilibirum

In addition to chiro's comment, what do you even mean by competitive equilibrium in a case of bilateral monopoly? There is nothing competitive in the scheme. This looks as though an Edgeworth box is needed, and usually then you get multiple feasible solutions. Moreover, your price comment baffles me because there are going to be two exchange ratios, one between labor and bicycles, and one between labor and wheat, and a price is nothing but an exchange ratio. Moreover, you can choose any one of the three as your numeraire (although it looks as if labor has implicitly been chosen as numeraire for you.)