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)

economyst · Answer

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.