Question

1. Mary’s utility preference for apples in comparison to all other goods is described by the function U(x,y) = xy, where x is the quantity of apples she has available to consume and y is the aggregate quantity of all other goods. Assume that Mary has 100 apples, $1,000 in cash on hand, and that a mixed bag of all other goods and services (anything but apples) can be purchased for $1 per bag.
   1. Calculate the numerical value of Mary’s U(x,y) function for her current endowment of apples and all other goods.
   2. Find ten other combinations of apples and cash that would result in the same numerical value of U(x,y) as the value found in (a).
   3. Graph the starting point and the other ten points found in (b)
   4. At the starting point (100 apples and $1000 cash) what is the value of Mary’s Marginal Rate of Substitution of apples for a composite of all other (non-apple) goods and services. Make a table in which you show the initial endowment and each of the 10 other combinations of quantities of apples and cash that you have identified as providing equivalent numerical values of Mary’s U(x,y) function, and calculate and record in your table the corresponding values of Mary’s Marginal Rate of Substitution of apples for the composite of all other goods.

Answer 1