[Step-by-Step] Assume that an individual has a utility function U=X Y. (The variable U is a hypothetical measure of the individual's level of satisfaction.
Question: Assume that an individual has a utility function \(U=X Y\). (The variable \(U\) is a hypothetical measure of the individual's level of satisfaction. A combination of \(X\) and \(Y\) that produces \(U=60\) connotes more satisfaction for the individual than a combination of \(X\) and \(Y\) that produces \(U=50\), for example.) Assume that the good \(X\) is pounds of Oreos and the good \(Y\) is quarts of milk.
Let his income be \(\mathrm{I}=\\) 20$ and the prices of the two goods be \({{\text{P}}_{\text{y}}}=1,\,\,{{\text{P}}_{\text{x}}}=2\). That is, the price of Oreos is $2.00 per package, and the price of milk is $1.00 a quart.
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Graph the indifference curves for \(U=40, U=50, U=60\), and \(U=100\). Use most of a graph paper page for your indifference map. Have at least ten plot points for each indifference curve. Constrain the values of \(X\) and \(Y\) such that \(0
- Find the combination of \(X\) and \(Y\) that will maximize consumer satisfaction (graphic procedure, so your graph must be accurate). What are the values of \(X\) and \(Y\) ? What is the value of \(U\) ? What is the slope of the budget line at your solution? What is the value for \(M R S_{x y}\) at your solution?
C. Still using the same graph, show graphically the new solution if the price of \(X\) changes so that \(P_{x}=1\). The individual's indifference map, income, and \(P_{y}\) stayed the same. What are the new values of \(X\) and \(Y\) ? What is the new value of U? What is the new slope of the budget line at your solution? What is the value for MRS \(_{x y}\) at your new solution?
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- Find the combination of \(X\) and \(Y\) that will maximize consumer satisfaction (graphic procedure, so your graph must be accurate). What are the values of \(X\) and \(Y\) ? What is the value of \(U\) ? What is the slope of the budget line at your solution? What is the value for \(M R S_{x y}\) at your solution?