A consumer maximizes utility. They have budget B, and purchase two goods, x1 and x2 ....

 

 

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A consumer maximizes utility. They have budget B, and purchase two goods, x1 and x2 . These goods can be purchased at prices P1 and P2. The consumer has utility function U = x23x7. a) Set up the Lagrangian function for this problem. b) Find the first order conditions. c) Solve for the demand curve for goods 1 and 2. d) Substitute the demand curves for goods 1 and 2 into the utility function to find the indirect utility function V (P1, P2, B) e) Find the otimal levels of the two goods the consumer will purchase when P1 = 4 and P2 =3 and B = $5000. f) What is the marginal utility of money in this example? Recall: this is the value of 1. g) Show that the result is a maximum. g) Show that the demand for good 1 is homogeneous of degree 0. A consumer maximizes utility. They have budget B, and purchase two goods, x1 and x2 . These goods can be purchased at prices P1 and P2. The consumer has utility function U = x23x7. a) Set up the Lagrangian function for this problem. b) Find the first order conditions. c) Solve for the demand curve for goods 1 and 2. d) Substitute the demand curves for goods 1 and 2 into the utility function to find the indirect utility function V (P1, P2, B) e) Find the otimal levels of the two goods the consumer will purchase when P1 = 4 and P2 =3 and B = $5000. f) What is the marginal utility of money in this example? Recall: this is the value of 1. g) Show that the result is a maximum. g) Show that the demand for good 1 is homogeneous of degree 0.

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g OHaty 0 x Total budgot Price of xi Price of x2 03 P P2 ... View the full answer