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)= XB0,5  YB0,5 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.

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