Graph the utility function U(S,A)= S^0.4*A^0.6 & show MU
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a) With a utility function of U(S,A)= S^0.4*A^0.6, derive a set of data points for U=1 and then plot a graph to show this indifference curve. Hint: use maximum values of 9 apples (A) and 27 sandwiches (S).
b) When U=1, and using a maximum value of 27 sandwiches (S) and 9 apples (A), calculate the marginal utility of S and A.
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Solution Summary
This solution shows how to use Microsoft Excel to graph the utility function U(S,A)= S^0.4*A^0.6. Calculations are made to derive a set of data points for the value U=1, and the resulting indifference curve is graphed. The solution then shows how to calculate Marginal Utility when U=1.
Solution Preview
a) Rewrite the equation as:
U = S^(2/5) * A^(3/5)
Let U = 1
1 = S^(2/5) * A^(3/5)
Because both exponents have a denominator of 5, raise both sides to the 5th power.
1^5 = (S^(2/5) * A^(3/5))^5
1 = S^2 * A^3
To solve for A:
1/(S^2) = A^3
(1/(S^2))^(1/3) = A
To solve for S:
1/(A^3) = S^2
(1/(A^3))^(1/2) = S
The formulas are used in the Excel file to solve for A when S>1, and to solve for S when A>1. Column D plugs the results back into the original function (with exponents of 0.4 and 0.6) to show that the result for U is always 1.
b) The marginal utility of apples is the ...
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