Question

From the first lecture, we have a person's utility function $$U(x_1, x_2) = x_1(A + Bx_2)$$ with budget constraint $p_1x_1 + p_2x_2 = I$, and A and B are constants greater than 0. 1. (1 point) Set up the Lagrangian. 2. (4 points) Find the first-order conditions of the utility maximization problem (Lagrangian method). 3. (4 points) Solve these first-order conditions to find the demand functions for goods 1 and 2. (Find the optimal quantity of goods 1 and 2 as a function of *Submit the solutions on Courselink. 1 $p_1$, $p_2$, and I.) Verify that this matches the solution we found in class via the substitution method. 4. (1 point) Find the expenditure functions of goods 1 and 2. Do they depend on prices?

          From the first lecture, we have a person's utility function
$$U(x_1, x_2) = x_1(A + Bx_2)$$
with budget constraint $p_1x_1 + p_2x_2 = I$, and A and B are constants greater than 0.
1. (1 point) Set up the Lagrangian.
2. (4 points) Find the first-order conditions of the utility maximization problem
(Lagrangian method).
3. (4 points) Solve these first-order conditions to find the demand functions for
goods 1 and 2. (Find the optimal quantity of goods 1 and 2 as a function of
*Submit the solutions on Courselink.
1
$p_1$, $p_2$, and I.) Verify that this matches the solution we found in class via the
substitution method.
4. (1 point) Find the expenditure functions of goods 1 and 2. Do they depend on
prices?

from the first lecture we have a persons utility function ux1 x2 x1a bx2 with budget constraint p1x1 p2x2 i and a and b are constants greater than 0 1 1 point set up the lagrangian 2 91628

Added by John M.

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