Problem 1 (45 pts) (Explain your answers!) Jim has the utility function u(x1, x2) = (2+x1)2 where x1 and x2 are the quantities of the two goods consumed, with respective prices p = 1 and p2. p1 (a) Find Jim's demand functions for any p2 > 0 and any m > 2. = (b) [harder] If p2 1, find the cheapest consumption bundle at which Jim achieves u(x1, x2) = 9. (c) Find Jim's optimal consumption bundle for p2 = 2 and m = 10. (d) Suppose, starting from p2 = 2 and m = 10, the government puts a $1 quantity tax on good 2. Find the income, substitution, and total effects of the resulting price change on the quantities demanded of goods 1 and 2. Is good 2 ordinary? Is good 1 inferior? Explain. 24 Suppose there are 30 consumers in total with the same preferences as Jim. 20 consumers have incomes m = 10 and 10 consumers have incomes m = 22. The market supply function for good 2 is qs (p2) = 11-p2 (e) Use your answers from part (a) to show that the market demand function for good 2 is q (p2) two points on the market demand curve for good 2. * * 240 Find = P2 (f) Find the equilibrium price, p and quantity, q of good 2. What is the price elasticity of demand at q? (g) Suppose a subsidy s = $1 is given per each unit of good 2 sold. Find the equilibrium quantity, the price paid by consumers, and the price received by producers after the subsidy. Explain how and why they differ relative to part (f).