Question 2 (6 points) Determine if completeness and transitivity are satisfied for the following preferences defined on x = (x], *) and y = (yj yz). (Hints: 1- You have to use z = (21, Zz) to prove or disprove transitivity. 2- You can disprove by a counter example) - x yiff > > yjor x, = y, and X, > y2- Question 3 (14 points) During the energy crisis of the mid-1970s a proposal was made to increase the tax on gasoline by 500 per gallon. The government would give poor consumers an amount of cash large enough that they could buy their original bundle (of gasoline and other goods). 1. Show how a typical poor person's budget line changes as a result of the tax and the subsidy. (3 points) 2. Use a graph to show how the tax and subsidy could affect this person's optimal bundle. (5 points) 3. Is this individual better or worse off or stay on the same bundle as a result of the tax and the subsidy? Explain your answer using your graph and show the possible scenarios. (6 points) Question 4 (7 points) A person's utility function is of the form U(x.y) = 5xy. The prices of good x and y are p, = $4 and p. = $2, respectively. The person's income is $1200. 1. What quantities of x and y should the consumer purchase to maximize his utility? (2 points) 2. Explain whether each of the two goods is normal or inferior. (2 points) 3. Derive the Engel curve for x. Draw it. (3 points) Question 5 (12 points) Helen spends all her money on food and clothing. When the price of clothing decreases, she ends up buying more clothing. (Note: In the following questions, be clear about the direction of the effect as increasing, decreasing, or ambiguous. And explain completely and explain the possible scenarios) 1. Does the substitution effect cause her to buy more or less clothing? Explain. (3 points)