Question

U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5

As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond to the minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Ci make sense from an economic standpoint?

Now let us connect the idea of economic utility to actual dollar values. To keep the values more manageable, we will use household income rather than the entire state budget, and retail costs and measures rather than industrial ones. Find the Median Household Income for Mesa, AZ for the most recent year possible. Then find the dollar cost in Mesa, AZ for a Penny, a pound of Ground Beef, a pair of Jeans, fresh Orange Juice, and a Movie Ticket. (Entertainment is often used as a stand-in for Climate.) A Cost-of- Living Index is a good place to find much of this data. Record these prices as P1, P2, P3, P4, and P5 respectively.

Construct an equation using Median Income, the Ci and Pi values that illustrates how much of each resource the Median Household can afford to purchase. Given this restriction, do the maximum or minimum values of U change? Do the values of Ci that give the maximum or minimum values change? What are these new values? How should the Median Household budget its Income so as to maximize its Economic Utility?

Write up your findings in a paper that you could turn in to an employer. Be sure to show all your work. Include any appropriate references as well as any computational devices used.

* Solve the questions, make the table, and the graph.

Answer 1

U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond to the minimum value of U? What values of Ci correspond to the maximum value of U?