Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by UD(q1,q2)=4lnq1 +q2 The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized p2 = 1 (a) Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?
Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by UD(q1,q2)=4lnq1 +q2 The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized p2 = 1 (a) Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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Darwin consumes cigarettes (x1) and other goods (x2). His preferences are given by
UD(q1,q2)=4lnq1 +q2
The quantity of good 2 is measured in units of income and so you can assume that throughout this problem, the price of good 2 is normalized
p2 = 1
(a) Using the Lagrangian, derive Darwin’s uncompensated demand for cigarettes: D1D(p1,Y). Note that we are holding p2 =1 and so that is not a variable in the demand function. Using the Lagrangian, derive the equation λ∗(p1, Y ). Provide an economic interpretation of the Lagrange multiplier. Does it vary with income, Y ?
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