Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions: UAhmet (XA,YA)= 5ln(XA)+ln(YA) UBerk (XB,YB)= XB 0.5 YB 0.5 a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents. b. Now assume that X is a public good, but Y is a private good. Write down the optimality condition for good X. Then, write down the optimal level of X as a function of Y for both agents. c. Now compare the consumption levels for X in parts a and b.