Suppose that a consumer has utility U(X,Y) = 2XY + X and income of $499 to spend on goods X and Y. The prices of X and Y are $1 and $2 per unit respectively. The optimal basket of goods is ____X and ____Y.

Question

Quizplus · Accepted Answer

To find the optimal basket of goods, we need to maximize the utility function U(X,Y) = 2XY + X subject to the budget constraint, which is $499 = $1*X + $2*Y. Solving the optimization problem using the method of Lagrange multipliers or by setting up the budget constraint to solve for one variable in terms of the other and then substituting back into the utility function, we find that the combination of X and Y that maximizes utility given the budget constraint and prices is 250 units of X and 124.5 units of Y.

Suppose That a Consumer Has Utility U(X,Y) = 2XY