Sarah makes $500 a week at her summer job and spends her entire weekly income on new running shoes and designer jeans. Because these are the only 2 items that provide utility to her. Furthermore, sarah insists that for every pair of jeans she buys, she must also buy a pair for shoes (without the shoes the jeans are worthless).

Therefore, she buys the same number of pairs of shoes and jeans in any given week. The shoes and jeans are indivisible; Therefore, with budget constraint, some possible adjustment to round down to the nearest integer is needed. Also, if you choose to graph the method to answer, in your diagrams, please put jeans (J) on the vertical axis and shoes (S) on the horizontal axis.

A) Please use a math function to express Sarah's utility function

B) If jeans cost $20 and shoes cost $30 how many will Sarah buy of each? What is her maximum utility?

Suppose that the price of shoes reduces to $20 a pair. How many shoes and jeans will she buy? What is her maximum utility?

Please explain to what effect (Income, substitution or both) do you attribute the change in her utility levels between part B and C.