1. John has income of $200 each month to spend on day passes to the gym (x) and food (y). Assume both of these goods are continuously divisible. A day pass to the gym costs $10 and food costs $1 per u

Econ 301: Homework Assignment 2 Fall 2018 Prof. Toohey Due by 5pm on Friday, September 21 You may work in groups of up to 3. Include the full names of anyone who worked on the assignment. Give the assignment to me in class or slide it under the door of my o ce (420 Purnell). Staple multiple sheets together. 1.John has income of $200 each month to spend on day passes to the gym ( x) and food ( y).

Assume both of these goods are continuously divisible. A day pass to the gym costs $10 and food costs $1 per unit.

(a)Draw a neat and well-labeled graph of John budget constraint.

(b)Suppose John health insurance company o ers a wellness plan that pays 50% of gym expenditure up to $40 each month. On another neat and well-labeled graph, draw John's new budget constraint.

(c)Assuming John spends his entire budget, the opportunity cost of an additional gym pass takes on two values at di erent points on the graph. What are those values?

2.Willie is throwing a party where he will serve lobster meat and shrimp. Both of these are sold by the pound and are continuously divisble. A pound of lobster meat costs $30 and a pound of shrimp costs $15. Willie has $180 to spend on lobster meat and shrimp.

(a)The store where Willie is shopping o ers a deal where anyone buying at least8 pounds of shrimp receives an extra 3 pounds of shrimp for free. On a neat and well-labeled graph, draw Willie's budget constraint. Place pounds of lobster on the horizontal axis and pounds of shrimp on the vertical axis.

(b)Suppose Willie has well-behaved preferences over bundles of lobster meat and shrimp. In three sentences or less, explain why Willie's optimal bundle would never contain exactly 10 pounds of shrimp.

3.Michael has preferences over two goods, x 1 and x 2, represented by the utility function u (x 1; x 2) = x2 = 3 1 x1 = 3 2 :

(a)Find the M RS 12associated with this utility function.

(b)Use the M RS 12, the price ratio, and the budget constraint to nd Michael's optimal bundle when m= 3000, p 1 = 50, and p 2 = 10.

(c)Find the equation of the indi erence curve containing the optimal point and solve it forx 2. (You will need to calculate the utility at the optimal point in order to do this.) (d)Graph the budget line, the optimal point, and the indi erence curve you just found on a single graph. Be sure to label the curves, the optimal point, and the axes.