# Quantitative Microeconomics

1. John has assets of \$200 anniversary ages to absorb on day passes to the gym (x) and aliment (y). Assume both of these appurtenances are continuously divisible. A day canyon to the gym costs \$10 and aliment costs \$1 per unit.  .  (a)  Draw a accurate and well-labeled blueprint of John account constraint.   .  (b)  Suppose John bloom allowance aggregation offers a wellness plan that pays 50% of gym amount up to \$40 anniversary month. On addition accurate and well-labeled graph, draw John’s new account constraint.   .  (c)  Assuming John spends his absolute budget, the befalling amount of an added gym canyon takes on two ethics at altered credibility on the graph. What are those values?   2. Willie is throwing a affair area he will serve lobster meat and shrimp. Both of these are awash by the batter and are continuously divisble. A batter of lobster meat costs \$30 and a batter of shrimp costs \$15. Willie has \$180 to absorb on lobster meat and shrimp.  .  (a)  The abundance area Willie is arcade offers a accord area anyone affairs at atomic 8 pounds of shrimp receives an added 3 pounds of shrimp for free. On a accurate and well-labeled graph, draw Willie’s account constraint. Place pounds of lobster on the accumbent arbor and pounds of shrimp on the vertical axis.   .  (b)  Suppose Willie has affable preferences over bundles of lobster meat and shrimp. In three sentences or less, explain why Willie’s optimal array would never accommodate absolutely 10 pounds of shrimp.   3. Michael has preferences over two goods, x1 and x2, represented by the account action u(x ,x )=x2/3x1/3.  12 12 (a) Acquisition the MRS12 associated with this account function.  .  (b)  Use the MRS12, the amount ratio, and the account coercion to acquisition Michael’s optimal bundlewhenm=3000,p1 =50,andp2 =10.   .  (c)  Find the blueprint of the alienation ambit absolute the optimal point and break it for x2. (You will charge to account the account at the optimal point in adjustment to do this.)   .  (d)  Graph the account line, the optimal point, and the alienation ambit you aloof begin on a distinct graph. Be abiding to characterization the curves, the optimal point, and the axes.

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