Normalisation of Prices:

See that we have one equation in  two unknowns, the prices. However, since we have a pure exchange economy without money, only relative prices matter, i.e., only  the price ratio is important. That means, we  can  "normalise"  on of the prices to 1 :Remark This  result  also comes  from  the  homogeneity of  degree  0 of the demand  functions. Remember;  by  definition of homogeneity of degree 0  in prices we  have:

Second Market:

We solve for the other market, i.e., the market for. good 2. By Walras law, if one market clears  the second also clears (if the total number of market is 2); thus using the prices computed above, we get the equilibrium demands for the market of good 2. Thus, from