Q: 1) If Px=5 and a person could buy (10,0) or (0,5) but either would take their entire income, what is the equation for the budget constraint? How many units of y is the market willing to trade for 1 x.
A: Since (10,0) takes all of their income we know that I/Px=10 or I/5=10 so I=50. Using this and the fact that I/Py=5 or 50/Py =5 we have Py=10. So the budget constraint is 50=5X+10Y. The slope of the B.C. is -Px/Py or -5/10 or -1/2. So the market is willing to trade 1/2 of a unit of y for 1 unit of x.
Q: if u(x,y)=x2y3, find the MRS.
A: MRS = MUx/MUy = 2xy3/3x2y2 = 2y / 3x.