Quantitative Microeconomics

1. John has allowance of $200 each month to waste on day ignoringes to the gym (x) and maintenance (y). Assume twain of these commodities are unintermittently separable. A day ignoring to the gym absorbs $10 and maintenance absorbs $1 per ace.  .  (a)  Draw a graceful and well-labeled graph of John budget engagement.   .  (b)  Suppose John bloom insurance community offers a wellness intent that pays 50% of gym outgoings up to $40 each month. On another graceful and well-labeled graph, describe John’s new budget engagement.   .  (c)  Assuming John wastes his undiminished budget, the turn absorb of an subjoined gym ignoring takes on two values at irrelative objects on the graph. What are those values?   2. Willie is throwing a plane where he obtain work-for lobster fruit and shrimp. Twain of these are sold by the triturate and are unintermittently divisble. A triturate of lobster fruit absorbs $30 and a triturate of shrimp absorbs $15. Willie has $180 to waste on lobster fruit and shrimp.  .  (a)  The place-of-business where Willie is shopping offers a bargain where anyone buying at meanest 8 triturates of shrimp receives an extra 3 triturates of shrimp for uncounted. On a graceful and well-labeled graph, describe Willie’s budget engagement. Place triturates of lobster on the insipid axis and triturates of shrimp on the upright axis.   .  (b)  Suppose Willie has well-behaved preferences aggravate parcels of lobster fruit and shrimp. In three sentences or close, decipher why Willie’s optimal parcel would never embrace precisely 10 triturates of shrimp.   3. Michael has preferences aggravate two commodities, x1 and x2, represented by the service discharge u(x ,x )=x2/3x1/3.  12 12 (a) Ascertain the MRS12 associated delay this service discharge.  .  (b)  Use the MRS12, the compensation narration, and the budget engagement to ascertain Michael’s optimal parcelwhenm=3000,p1 =50,andp2 =10.   .  (c)  Find the equation of the triviality incurvation embraceing the optimal object and reresolve it for x2. (You obtain scarcity to count the service at the optimal object in regulate to do this.)   .  (d)  Graph the budget row, the optimal object, and the triviality incurvation you equitable endow on a uncombined graph. Be trusting to delineate the incurvations, the optimal object, and the axes.