Question

Suppose that a typhoon occurs each year with a probability 1/12 and that a typhoon will destroy bananas from exactly half the farmers who choose to plant in a particular year. Calculate the expected profit of each farmer (including the planting costs) if exactly 110 farmers enter the market, and each chooses to plant 12,500 kgs of bananas. Explain why you would expect additional farmers to enter the market when typhoons are possible. Discuss what this implies for equilibrium prices in years where a typhoon does not occur.

Answer 1

Expected profit (presented in units of Kg):

Table of computation

Status	Qty.	Probability	Expectation
No typhoon	12,500	1 – 1/12 = 11/12	12,500 × 11/12 = 11,458
With typhoon	12,500 × ½ = 6,250	1/12	6,250 × 1/12 = 521
		Total = 1	Total = 11,979

Answer: expected profit is 11,979 kg.

Additional farmers:

They are expected to enter the market, because the probability of typhoon is very low (only 1/12). This much of risk is almost there in any sort of business.

Moreover, if there is typhoon all the products would not be damaged but only ½ portions would be damaged. This creates shorter supply in the market, the supply curve would shift to the left, the equilibrium would be at higher price, and therefore firms would sell products at higher price. Such higher price compensates the loss of goods damaged.