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

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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 provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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