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Finding the optimal consumption bundle

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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.

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https://brainmass.com/economics/utility/finding-optimal-consumption-bundle-498456

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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.

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See Also This Related BrainMass Solution

Optimal Consumption Bundle using the Lagrangian Method

Kaidu consumes two goods, x_1 and x_2, with respective prices p_1 and p_2. His utility function is given by U_Kaidu (x_1,x_2 )=x_1^(1/4) x_2^(3/4) . Let p_1=5 and p_2=4. Kaidu's income is 80.

- Suppose the government imposes a $1 tax each unit consumption of x_2, solve for the new optimal consumption bundle.

How do i obtain this? Is the Lagrangian Method used and if so, then how?

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