. Remox Corporation is a British firm that sells high-fashion sportswear in the United States. Congress is currently considering the imposition of a protective tariff on imported textiles. Remox is considering the possibility of moving 50 percent of its production to the United States to avoid tariff. This would be accomplished by opening a plant in the United States. The following table lists the profit outcomes under various scenarios:
Profit in 2008
No Tariff Tariff
Option A: Produce all output in Britain $1,200,000 $ 800,000
Option B: Produce 50% in the United States $ 875,000 1,000,000
Remox hires a consulting firm to assess the probability that a tariff on imported textiles will in fact pass a congressional vote and not be vetoed by the president. The consultants forecast the following probabilities:
Probability
Tariff will pass 30%
Tariff will fail 70
a. compute the expected profits for both options.
b. based on the expected profit only, which option should Remox choose?
c. Compute the probabilities that would make Remox indifferent between options A and B using that rule.
d. Compute the standard deviations for options A and B facing Remox Corporation.
e. What decision would Remox make using the mean-variance rule?
f. What decision would Remox make using the coefficient of variation rule?
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a. To compute the expected profits for both options, we will multiply the profit outcomes with their respective probabilities.
Option A (Produce all output in Britain):
Expected Profit = (Profit with No Tariff * Probability No Tariff) + (Profit with Tariff * Probability Tariff)
Expected Profit for Option A = ($1,200,000 * 0.70) + ($800,000 * 0.30)
Option B (Produce 50% in the United States):
Expected Profit = (Profit with No Tariff * Probability No Tariff) + (Profit with Tariff * Probability Tariff)
Expected Profit for Option B = ($875,000 * 0.70) + ($1,000,000 * 0.30)
b. Based on the expected profit only, Remox should choose the option with the higher expected profit. Therefore, Remox should choose Option B if the expected profit for Option B is higher than the expected profit for Option A. Otherwise, Remox should choose Option A.
c. To determine the probabilities that would make Remox indifferent between options A and B, we need to set their expected profits equal to each other and solve for the probability of the tariff passing.
Expected Profit for Option A = Expected Profit for Option B
($1,200,000 * (1 - Probability Tariff)) + ($800,000 * Probability Tariff) = ($875,000 * (1 - Probability Tariff)) + ($1,000,000 * Probability Tariff)
Solving this equation will give us the probabilities at which Remox would be indifferent between options A and B.
d. To compute the standard deviation for options A and B, we need to calculate the variance and then take the square root of the variance.
Variance = [(Profit with No Tariff - Expected Profit)^2 * Probability No Tariff] + [(Profit with Tariff - Expected Profit)^2 * Probability Tariff]
Standard Deviation = √Variance
Compute the variance and standard deviation for options A and B to determine their risk.
e. The mean-variance rule states that a decision-maker should consider both the expected profit and the risk (measured by the standard deviation). If Remox Corporation follows the mean-variance rule, they will choose the option that maximizes the expected profit while minimizing risk. Therefore, Remox will choose the option that has the highest expected profit and the lowest standard deviation.
f. The coefficient of variation rule takes into account both the expected profit and the risk but measures risk relative to the expected profit. It is calculated by dividing the standard deviation by the expected profit.
Coefficient of Variation = Standard Deviation / Expected Profit
Compute the coefficient of variation for options A and B. Remox will choose the option with the lowest coefficient of variation, indicating the lowest level of risk relative to the expected profit.