In: Economics
Assume that Japan and Korea can switch between producing cars and producing airplanes at a constant rate. Hours Needed to Make 1 Quantity Produced in 2400 Hours Car Airplane Car Airplane Japan 30 150 80 16 Korea 50 150 48 16 Which Amount of production is not possible for korea given 2400 hours? A. 0 cars 12 airplanes B. 48 cars 16 airplanes C. 24 cars 8 airplanes D. 48 cars 0 airplanes
Solution:
For Korea, we are given that hours needed to make 1 car is 50 while hours needed to make 1 airplane is 150. Correspondingly, in 2400 hours, it can either produce 48 cars or 16 airplanes.
Then, the opportunity cost of producing 1 airplane = 48/16 = 3 cars for Korea
Opportunity cost is simply the slope of a production possibility frontier, and now we can write the function for Korea's PPF as follows:
Using straight line equation: y = mx + c, where m is slope and c is vertical intercept, we can write Korea's straight line PPF function (straight line as we are given that production switch is constant) as:
With cars on vertical axis and airplanes on horizontal axis, C = -3*A + 48 where C is quantity of cars produced and A is quantity of airplanes produced.
C = 48 - 3A
Any of the given combinations lying outside of this line is impossible to be produced by Korea.
As maximum plane production is 16, with 0 cars, 12 airplanes can obviously be produced. Similarly, as maximum car production is 48, with 0 plane production, 48 cars can be produced. So eliminating options A and D.
For option C, with 8 airplanes, cars that can be produced = 48 - 3*8 = 24 cars, which is as given in option, so this production combination is possible.
The impossible production point is 48 cars and 16 airplanes, as thinking logically, when country employs all its hours in production of planes, it is able to produce 16 airplanes. In other words, not a single hour is left for car production, and thus not a single car can be produced, let alone 48 cars. Similar argument can be presented from car point of view aa well.
Thus, the correct option is (B).