Question 1: Suppose that there are 3 firms, each offering a single type of milk (always in 1-quart containers) that is horizontally differentiated along a single dimension, the percent of fat. Firm-1 offers nonfat milk, with 0% fat. Firm-2 offers low fat milk, with 10% fat. Firm-3 offers high fat milk, with 50% fat. There are 1,000 potential consumers. Some consumers hate fat and some love it. But the most fat any individual consumer would ideally have in their milk is 50%. In particular, assume that people's tastes for the ideal percent of fat is uniformly distributed from 0% to 50%. That is, the line starts at zero and goes to 50 (instead of 1 as we have done in the past). The utility that individual i obtains from purchasing a quart of milk from seller j is given by uij = 5 - Pj - 10 Ti - xj where xi belonging to [0, 50]: individual i's ideal fat content, xj belonging to [0, 50]: fat content offered by firm j. Assume also there are no fixed costs for any of the firms. Marginal costs for each firm are 0.5, 0.3 and 0.7, respectively for firms 1, 2 and 3. a) Derive the demand functions for each of the firms.