Janice is producing a new product at marginal cost of £1, and by law she has to sell it for £2. She has to decide how much to produce before she learns the demand. All she knows is that demand will be 20 or 50, with equal probability. If she is just a little bit risk averse, how many units should she produce?

Question

Janice is producing a new product at marginal cost of £1, and by law she has to sell it for £2. She has to decide how much to produce before she learns the demand. All she knows is that demand will be 20 or 50, with equal probability. If she is just a little bit risk averse, how many units should she produce?

(A) 20 units.
(B) 50 units.
(C) 49 units.
(D) 34 units.
(E) None.

(Solution is A, 20 units)

Answer 1

If she makes 20, she sells all 20 and makes 20 profit.

If she makes 50 there is a .5 chance she sells all 50 and makes a 50 profit, and a .5 chance she sells 20, throws 30 in the trash and makes a 10 loss. Her expected profit is .5*50 + .5*(-10) = 20.

Since the sure-thing of option A makes 20 and the risky option makes of option B makes 20 and since she is a bit risk averse, option A is better than option B.

Just to be sure, repeat for options C and D.

Answer 2

To determine the optimal quantity to produce, we need to consider the expected profit for each potential quantity. Since the demand can be either 20 or 50 with equal probability, there are two potential scenarios to consider:

Scenario 1: Demand is 20
If the demand is 20, Janice's profit will be £2 (selling price) minus £1 (marginal cost) multiplied by 20 (quantity sold). This gives us a profit of £40.

Scenario 2: Demand is 50
If the demand is 50, Janice's profit will be £2 (selling price) minus £1 (marginal cost) multiplied by 50 (quantity sold). This gives us a profit of £100.

To calculate the expected profit, we need to weigh the profits from each scenario by their corresponding probabilities. Since both scenarios have an equal probability of occurring, the expected profit is:

(£40 + £100) / 2 = £140 / 2 = £70

Now, considering that Janice is risk-averse, she will want to optimize her expected profit while minimizing the risk of losses. This means she will likely err on the side of caution and choose a quantity that maximizes her minimum profit.

In this case, producing 20 units would give Janice a minimum profit of £40 if the demand is 20. This minimum profit is higher than the minimum profit of £50 if she were to produce 50 units.

Therefore, Janice should produce 20 units (option A) to be risk-averse and maximize her expected profit while minimizing the risk of losses.