Suppose the consumers in an economy have monotone preferences. Show the follow- ing two things: . All prices are strictly positive. . If the market for good 1 clears then so does the market for good 2. Hint: for the first two bullet points, proceed by contradiction. That is, if you assume a price is zero argue that the market clearing conditions cannot hold. For the last bullet 2 point combine the budget constraints with the market clearing condition, and use that prices are strictly positive (as shown in bullet 1). Remark: This last result is what we call "Walrass's Law". It states that in an economy with N markets (in this case, N=2) then only N-1 markets are linearly independent. As such, we can calculate at most N-1 absolute prices. As a consequence, we have one degree of freedom to choose arbitrarily one of the prices, and then all other prices are calculated relative to that one price arbitrarily chosen. For example, in a 2 good economy, we can arbitrarily choose the price of good 1, and then the price of good 2 will be expressed relative to good 1