Q15. Consider the following objective function of two variables X and Y (note that this is like a utility function) U(X,

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Q15 Consider The Following Objective Function Of Two Variables X And Y Note That This Is Like A Utility Function U X 1 (104.61 KiB) Viewed 14 times

Q15. Consider the following objective function of two variables X and Y (note that this is like a utility function) U(X,Y)= log(X) + log(Y) The two variables must satisfy the following linear relationship (note that this is like a budget constraint) 20X10Y = 100 3 (1) Write down the maximization problem subject to the constraint. Use the constraint to solve for Y as a function of X. Plot this equation with X in the horizontal axis and Y in the vertical axis. What is the slope of this line? (3) Replace Y the expression above into the objective function U and re-write the maximization problem, which now should only depend on X. (4) Find the optimal value of X. To do this, take the derivative of the objective function found in part 3. with respect to Xand make it equal to zero. Then solve for X. (5) Using the expression in 2 and the optimal value of X found in 4, find the optimal value of Y. (6) Using the optimal value of X and Y, find the value of the objective.