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 $1800 per month. Further, suppose that the price of good 1 is p1=$6 and the price of good 2 is p2=$3. Finally, suppose that the tastes of the household are described by the utility function (₁, ₂) = ₁^1/2 ₂^3/2, where ₁ denotes the quantity of good 1 and ₂ the quantity of good 2.

Questions:

1. In a 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. In a graph with good 1 on the horizontal axis and good 2 on the vertical axis, what is the value of the horizontal intercept of the budget constraint?

3. Do the indifference curves of the household intersect the axes?

a. Yes, they intersect both axes

b. They intersect only the vertical axis

c. No, they do not intersect the axes

d. They intersect only the horizontal axis

5. What is the value of the MRS at bundle (1,6)? [Hint: u1 = 1/2₁^-1/2 ₂^3/2 and u2 = 3/2₁^1/2₂^1/2. Note: When asked the value of the MRS at a given bundle, please insert a negative number if you find that the MRS is negative.]

6. What is the optimal quantity of good 1 purchased by the household?

7. What is the optimal quantity of good 2 purchased by the household?

8. Now suppose that the government introduces a voucher system to support families whose monthly income is lower than $3000. 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 used to buy good 2. Suppose that this family receives $900 in vouchers per month. What is the optimal quantity of good 1 purchased by the family after the introduction of the voucher system?

9. What is the optimal quantity of good 2 purchased by the family after the introduction of the voucher system?