2 Long questions 1. Consider a consumer who consumes three goods, the quantity consumed for good 1, 2 and 3 are $1, 12 and x3 respectively. The utility function of the consumer is U = x3 + x2 + x3. The price of good 1 is 1, price of good 2 is 1, and price of good 3 is 4. The consumer has income 20. (a) What is the budget constraint for the consumer? (b) What is the quantity of consumption that maximise the utility of the consumer? (c) The markets for good 1 and 2 are now dominated by a single firm - the firm now only sells good 1 and 2 in a bundle that, for each unit of good 1 purchased, the consumer has to purchase two units of good 2. Is the utility maximising quantity that the consumer would have purchased in part (b) available in this new circumstances? Discuss how you could find the utility maximising quantity of consumption for the consumer, without solving for it explicitly. (d) In light of part (c), what are the economic assumption(s) you made in part (a) of the question? Are they reasonable assumption (s) in real life? Discuss why or why not