Consider a monopolist selling a product with inverse demand of P_D=12Q. The firm currently has production costs of C(q)=5+6Q. The firm has the option of attempting to develop a new technology that would lower production costs to C(q)=5+2Q. Research and development costs are $4 if undertaken and must be incurred regardless of whether or not the new technology is "successful" or a "failure." This means that in case of failure, the firm still needs to produce with C(q)=5+6Q but incurs $4 in sunk costs. If the firm attempts to develop the new technology, the innovation will be successful with probability p=3/8. Throughout your analysis, restrict attention to the profit/loss of the firm in only the current period (i.e., assume that the firm will not be operating in any future period).

Assume the monopolist could consult an engineer who, while not being able to provide perfect information, can evaluate the new technology as either "Promising" or "Risky." You then update your preferences. If P(Success)P(Promising|Success) = 0.3, what is then the updated probability of P(Risky | Success)?

Question 47 options:

1/10

2/10

3/10

4/10