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Give the formula for valeries mrs of x for y

Problem

Valerie wants to exercise and has a choice of going to an aerobics class, which costs $3 each time, or to the gym where she can work out with weights; the gym costs $2 per visit. She likes to do some of each type of exercise; that is, the more aerobics she does, the more she enjoys weightlifting, and vice versa. However, University of California Economics 100A Department of Economics Professor K Train Page 3 of 5 she enjoys aerobics, even if she never lifts weights, while weightlifting is fun for her only if she also does some aerobics. The following utility function reflects Valerie's preferences: u = xy + 4x where x is the number of aerobics classes per semester y is the number of visits to the gym for weightlifting per semester (Think about how this utility function represents Valerie's preferences as they have been described.) Valerie's budget for exercising is $100 per semester. We want to determine the number of aerobics classes and visits to the gym that she will choose. Or, stated another way, we want to determine the number of aerobics classes and visits to the gym that will make her most happy given her budget of $100. We will go through this exercise step-by-step: a) Give the formula for Valerie's budget constraint. (Express the constraint as y equaling some formula involving x.) b) Give the formula for Valerie's MRS of x for y. This is done in three steps: (i) Give the formula for her MUx. (Hint: calculate the increase in U due to increasing x by 1 unit: [(x+1)y + 4(x+1)] - [xy + 4x]) (ii) Give the formula for her MUy. (iii) Using (i) and (ii), give the formula for her MRS. (iv) Now: state in words what this MRS means, using "gym visits" and "aerobics classes" instead of x and y.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.

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