Consider a remote island country with a population of 80 people. The country only has the ability to produce two goods: apples and bananas. Producing a basket of apples requires 2 workers. Producing a basket of bananas requires 8 workers. There is no multi-tasking, meaning that an individual cannot be employed in more than one activity at the same time.

(a) Define the number of baskets of apples and bananas produced as QA and QB respectively. Define the number of workers producing apples and bananas as NA and NB. Write down the production possibilities boundary (PPB) for this economy. That is, derive the formula for the curve that shows the alternative combinations of baskets of apples and bananas that can just be attained if the entire population is working in one activity or the other.

(b) Graph the PPB you derived in part (a). Graph baskets of apples on the vertical axis and baskets of bananas on the horizontal axis. Be sure to calculate and identify the apple and banana intercepts in your graph.

(c) What is the opportunity cost of producing a basket of bananas if the economy is operating on the PPB?

(d) Imagine that the country discovers a new banana seed variety that doubles the productivity of banana production. That is, with the new variety, producing a basket of bananas requires only 4 workers. Repeat the exercises in parts (a)-(c) assuming the economy uses the new banana seed variety in production.

(e) Imagine that the country experiences a climatic change that reduces the productivity of both apple and banana production by 50 percent from what it was in part (d). That is, in the new environment each basket of apples and bananas produced requires 4 and 8 workers respectively. Repeat the exercises in parts (a)-(c) for this new environment. How has the opportunity cost of producing bananas changed from the value you derived in part (d)? Explain this result.