Robin’s utility function is , where and . Suppose the price of X is $12 and Y $15. Given that this is a Cobb-Douglas utility function, the tangency condition holds at the optimal bundle, where

Suppose the market demand curve is

Robin’s utility function is , where and . Suppose the price of X is $12 and Y $15. Given that this is a Cobb-Douglas utility function, the tangency condition holds at the optimal bundle, where

Suppose there are two goods, L and G. Lanier likes more of G and dislikes more of L. The Marginal Rate of Substitution (MRS) of Lanier’s indifference curves over L and G is:

The demand function for mangos is given by:

You ARE required to show work for this problem. Verify the identity below by using fundamental identities to transform the left-hand side of the equation into the right-hand side. Clearly show all steps on your own paper, with the problem number clearly labeled. Click “yes” when you have finished writing your solution to this problem.  identity 1.jpg   

Which of the following is a true statement about U.S. job gains and losses under the free trade agreements that the U.S. has participated in?

You ARE required to show work for this problem. Use long division to divide:  long division A.jpg   The quotient is: The remainder is: NOTE: You should type your answers in the blanks above as something like x^3 + x^2 + 1. Please clearly label the problem number. You should scan and upload your work after you have completed all of the problems on this exam.

You ARE required to show work for this problem. Use the properties of logarithms to expand the given expression as much as possible:  Properties of log final.png Write your answer on your paper, with the problem number clearly labeled. Click yes when you have completed this problem.  

You ARE required to show work for this problem. Find the exact radian solutions in the interval