Suppose that a consumer has the utility function given by U(X,Y) = 20X + 8Y + XY the prices of good X and Y are given by px = 5 TL and py = 1 TL the total budget the consumer has is / = 200 TL a) write down the consumer's optimization problem (formally) b) apply the langrangian method and solve the optimization problem (find the quantities of goods X and Y that maximizes consumer's utility subject to the budget constraint. apply the following steps: b.1) write the langrangian function b.2) write the first order conditions (FOC) b.3) find the values of X and Y that satisfy the (FOC).
Suppose that a consumer has the utility function given by U(X,Y) = 20X + 8Y + XY the prices of good X and Y are given by px = 5 TL and py = 1 TL the total budget the consumer has is / = 200 TL a) write down the consumer's optimization problem (formally) b) apply the langrangian method and solve the optimization problem (find the quantities of goods X and Y that maximizes consumer's utility subject to the budget constraint. apply the following steps: b.1) write the langrangian function b.2) write the first order conditions (FOC) b.3) find the values of X and Y that satisfy the (FOC).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose that a consumer has the utility function given by U(X,Y) = 20X + 8Y + XY
the prices of good X and Y are given by px = 5 TL and py = 1 TL
the total budget the consumer has is / = 200 TL
a) write down the consumer's optimization problem (formally)
b) apply the langrangian method and solve the optimization problem (find the quantities of goods X and Y that maximizes consumer's utility subject to the budget constraint. apply the following steps:
b.1) write the langrangian function
b.2) write the first order conditions (FOC)
b.3) find the values of X and Y that satisfy the (FOC).
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