2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...

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2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...

2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem.

a) Set up the Lagrangian function.

b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution.

c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget line at the optimal solution.

d) Derive Bob’s demand functions for good 1 and for good 2.

e) Is good 1 a normal good for Bob? f) Now assume that c=1/4 and d=3/4, m=160, p1=4 and p2=2. Calculate the income and substitution effects from an increase in price of x1 from p1=4 to p1=5.

g) Illustrate these effects in a graph.

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g) ma o n C+d) P, eel ズP,

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