Share
Explore BrainMass

Finding the optimal consumption bundle

Two consumers, Mamoon and Kader, consume only two goods, good 1 and good 2, with the quantities of each consumed denoted by x1 and x2 respectively. The price of x1 is $6/unit, and the price of x2 is $5/unit. The consumer has a fixed income of $64.

Mamoon has a utility function: U(x1,x2 )=2x1^3 x2^5?
Kader's utility function is: U(x1,x2 )=x1+2x2

a. Solve Kader's utility maximization problem.
b. Show the on a diagram with the horizontal axis represents x1and the vertical axis represents x2 the way to find the optimal consumption bundle of Kader graphically, label the optimal bundle.

Attachments

Solution Preview

Please refer attached file for graph.

a. Solve Kader's utility maximization problem.
U(x1,x2)=x1+2x2
Marginal utility of x1 can be found by differentiating with respect to x1.
MU(x1)=dU(x1,x2)/dx1=1

Marginal utility of x2 can be found by differentiating with respect to x2.
MU(x2)=dU(x1,x2)/dx2=2

Marginal Utility of x1 per dollar spent=MU(x1)/Px=1/6=0.167
Marginal Utility of x2 per dollar ...

Solution Summary

The solution describes the steps to solve the given utilization problem.

$2.19