Answer to Question #157879 in Microeconomics for natasea

Question

1.      Xan is a rational consumer who has an income of $11. He wishes to purchase both goods X and Y. Both goods are sold for $1.

(a)   Show that the condition for constrained utility maximization is satisfied. 

(b)  How much of good X and Y the individual should purchase to maximize utility if he spends all of his income.

(c)   Assuming that the individual has only the $11 to spend, determine the total utility the individual receives when he maximizes utility.

Units MUx MUy

1 15 12

2 11 9

3 9 6

4 6 5

5 4 3

6 3 2

7 1 1

Answer 1

(a) The condition for constrained utility maximization is satisfied, when

$MUx/Px = MUy/Py.$

(b) The individual should purchase 6 units of good X and 5 units of good Y to maximize utility if he spends all of his income.

(c) Assuming that the individual has only the $11 to spend, the total utility the individual receives when he maximizes utility is TU = TUx + TUy = (15 + 11 + 9 + 6 + 4 + 3) + (12 + 9 + 6 + 5 + 3) = 48 + 35 = 83 units.