Sheldon Leonard and Raj can do two and only two things with

Sheldon, Leonard and Raj can do two and only two things with their 400 hours of work each month: do lab experiments or make science fiction movies. All units are infinitely divisible.

In a month’s time Sheldon can do 40 lab experiments and make zero science fiction movies, or 40 science fiction movies and zero lab experiments, or any linear combination of these two extremes.

Leonard is different. He can do 60 science fiction movies and do zero lab experiments, or 44 science fiction movies and 32 lab experiments, or any linear combination between these two points. However, once he reaches 32 lab experiments he loses a little bit of interest. Beyond that point, he can make 44 science fiction movies and 32 lab experiments, zero science fiction movies and 54 lab experiments and all the linear combinations of these two points lying in between.

Raj is similar to Leonard. He can create 25 science fiction movies and do zero lab experiments, 15 science fiction movies and 30 lab experiments, or any linear combination between these two points. However, once he gets to 30 lab experiments, he tires, and from this point on, each lab experiment costs him 3 science fiction movies. Therefore, he can conduct a maximum of 35 lab experiments, at which time he produces zero science fiction movies.

a. Putting NUMBER OF SCIENCE FICTION MOVIES on the VERTICAL axis and NUMBER OF LAB EXPERIMENTS on the HORIZONTAL axis, graph the individual production possibility frontiers for Sheldon, Leonard and Raj in three separate graphs.

b. Imagine a world with only 2 people- Sheldon and Leonard. In this situation, suppose you start out with no lab experiments. How many science fiction movies are being made? Whom would you ask to do the first lab experiment in this world? Whom would you ask to do the last lab experiment in this world?

c. The public relations team wants to determine the efficient joint production possibilities frontier in a world with all three people. Putting NUMBER OF SCIENCE FICTION MOVIES on the VERTICAL axis and NUMBER OF LAB EXPERIMENTS on the HORIZONTAL axis, sketch out the efficient joint production possibilities frontier.

Solution

a) The following schedules can be drawn to attain PP curves.

Production Possibility schedule of Sheldon

Production Possibility Schedule for Leonard

Production Possibility Schedule of Raj

b.

In this case, Leonard should produce science fiction movies. Sherdon should od first experiment and Leonard should do last experiment. It is so because Leonard\'s efficiency is high in production of Science fiction movies and Sherdon\'s efficiency is high in case of lab experiments.