Consider a simple two-good model, where good x represents the good fuel and good y represents the composite good. Assume that the price of one unit of fuel is equal to px = 2 and that the price of one unit of composite good is equal to py = 1.

Point (a) to (g) have been answered, and they are listed here just to provide necessary information. If possible, please show the solutions starting from point (h).

(a) On a graph, illustrate the budget constraint of a family with income I

(b) What is the opportunity cost of fuel in terms of the composite good? Explain.

(c) Now assume that the price of fuel increases to px = 3. On the same graph illustrate the new budget constraint of a family with income I. What is the new opportunity cost of fuel in terms of the composite good?

(d) Governments are often reluctant to pass on the full impact of fuel prices to consumers. Assume that the government wants to introduce a subsidy of 1 dollar (s = 1) so that the price of fuel after the subsidy stays at px = px s = 3 1 = 2. You are asked to estimate the cost to the government of the subsidy policy. What information do you need?

(e) Keep assuming the new price of fuel is px = 3. After getting the estimate on the cost of the policy, the government proceeds to implement the proposed policy of subsidy s = 1. (Refer to this policy as policy A). Consider a household(householdP) and assume that it consumes the basket (xP =50,yP =100). What is the income of household P (call it IP ), and what is the MRS(x,y)(50, 100)? Explain.

(f) Keep assuming that the new price of fuel is px = 3 and s = 1. Consider another household (household R) that consumes the basket (xR = 500, yR = 1000). What is the income of household R (call it IR), and what is the MRS(x,y)(500,1000)? Explain.

(g) Now assume that there are only these two households in the country. What is the total cost for the government of policy A? (h) Find a policy that costs the same amount of policy A and that makes both households better off. Describe this policy as precisely as possible. Illustrate it graphically. (Refer to this policy as policy B)

(i) If you compare policy A and policy B, is it correct to say that policy B Pareto improves over policy A? Explain. Why do you think that in the real world governments do not use policy B and prefer using policy A? (j) Assume that both households have the same utility function u(x, y) = xy. Check that this utility function is consistent with the baskets chosen by the two households (see above points e) and f)). Explain.

(k) Keep assuming that both households have the same utility function u(x, y) = xy. Consider the following policy C, which is alternative to both policy A and policy B: Policy C simply requires to transfer the same amount of cash to both households. Assume that C has the same cost for the government of A and B. Find the basket consumed by the two households. (Warning: if you find results that are not integers, but fractions do not worry.) (l) Does policy C Pareto improve over policy A. Explain. (m) In what sense is policy C preferable to A and B?