Note4 - Utility Maximization Budget Constraint Let px =...

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Utility Maximization Budget Constraint Let p x = price of good x; p y = price of good y; and I = income. The budget constraint is given by p x x + p y y = I: What is the shape of the budget constraint? What is the slope of the budget constraint? What will be the shape of the budget constraint if p x depends on x (e.g., p x = px ) ? In a barter economy, what will be the budget constraint if the endowments are x 0 and y 0 ? Utility Maximization max x;y U ( x;y ) subject to p x x + p y y = I: To the consumer, income and prices are exogenous variables. The solution to the maxi- mization problem may be (i) interior, (ii) at a corner, or (iii) non-unique. Method 1: Lagrangian Method Form the Lagrangian L = U ( x;y ) + ( I p x x p y y ) ; where is called the Lagrangain multiplier. If the maximization problem has an interior @ L @x = @U ( x;y ) @x x = 0 ; (13) @ L @y = @U ( x;y ) @y y = 0 ; (14) @ L = I p x x p y y = 0 : (15) 14
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Note4 - Utility Maximization Budget Constraint Let px =...

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