(b) Why do we restrict X to lie in the interval (0,10) when we write the
PPF as a function? We restrict X to lie in the interval (0, 10) because all
other values less than 0 are in the negative region and 10 is the
maximum number of the nut produce that are available.
(c) Is the point (5, 100) [i.e., X=5, Y=100] an efficient amount of production
for Jane? Why or why not? This is not an efficient amount of production
because when X is 5, there can be 225 units of Y. So, she is not using her
(d) Sketch the PPF. Divide the diagram into three sets, as follows: points that
are attainable but inefficient; points that are attainable and efficient; points
that are unattainable.
(e) What is the opportunity cost of nuts at (4, 264)? What is the opportunity
cost of juice at the same point? Repeat both questions at (8,96). How are
these costs related to calculus concepts that you have learned? How are they
related to geometric properties of the graph that you have sketched?
(queston will be on exam)***
The opportunity cost of nuts = -dY/dX = - (-30 – 2x) = 30 + 2X
Opportunity cost of juice = -dX/dY = 1/(30 + 2X) (inverse)
For point (4, 264)
-dY/dX = 30 + 24 = 38L of juice
-dXdY = 1/ (30 + 2X) = 1/38 Kilos of nuts
Therefore the opportunity 38L of juice is 1/38Kilos of nuts.
For point (8, 96)
-dY/dX = 30 + 2X = 30 + 16 = 46L of juice
-dX/dY = 1/(30 + 2X) = 1/46 Kilos of nuts
The opportunity cost of 46L of juice is 1/46 kilos of nuts.
Theses costs are related to calculus concepts that I have learned because it
involves maximizing profit. They also relate to the properties of graphs because I
need to know things such as the zeros, intercepts, shapes of graphs and max/min
point. The slope of the tangent is the opportunity cost.