Problem 1 Text: A family has to decide how much of their monthly income to spend on good 1 and good 2. Suppose that this household has a fixed income of 53600 per month. Further, suppose that the price of good 1 is p,;=512 and the price of good 2 is p,=56. Finally, suppose that the tastes of the household are described by the utility function u(x,, x.) = xfxg, where , denotes the guantity of good 1 and X, the quantity of good 2. Questions: 1. Ina graph with good 1 on the horizontal axis and good 2 on the vertical axis, what is the value of the vertical intercept of the budget constraint? 2. Inagraph with good 1 on the horizontal axis and good 2 on the vertical axis, what is the value of the harizontal intercept of the budget constraint? 3. Do the indifference curves of the household intersect the axes? Yes, they intersect both axes Mo, they do not intersect the axes They intersect anly the vertical axis They intersect only the horizontal axis e nooow 4, Do the tastes of the household satisfy the 5 standard assumptions about tastes introduced in the lectures? Mo, monotanicity is violated Mo, convexity is violated Yes, they do There is not enough information to answer angow ~ 1 1.2 . XX, Mote: 1 3 3 1 What is the value of the MRS at bundle (1,9)7? [Hint: ML, = %xi zxg and MU; = 5 When asked the value of the MRS at a given bundle, please insert a negative number if you find that the MRS is negative. ] What is the optimal quantity of good 1 purchased by the household? What is the optimal quantity of good 2 purchased by the household? Mow suppase that the government introduces a voucher system to support families whose manthly income is lower than $6000. Vouchers have a dollar value that can be used to buy good 1 as if they were cash, but they cannot be used for anything else. In particular, they cannot be wsed to buy good 2. Suppose that this family receives $1800 in vouchers per maonth. What is the optimal guantity of good 1 purchased by the family after the introduction of the voucher system? What is the optimal guantity of good 2 purchased by the family after the introduction of the vaucher systermn