Question

Apple (A) and Blackberry (B) compete in the market for smartphones. Both firms have to decide whether they want to engage in R&D for a new type of device with a 3D enabled haptic touchscreen. Because A is relatively more efficient in R&D, fixed costs for this R&D project are $10mn for A and $15mn for B. Both firms are equally likely to come up with a marketable innovation (probability p). Expected profits from the new technology are $15mn if one firm manages to be alone in the market and $5mn each if both firms come up with a product. We assume that there are no variable costs.

What is the expected payoff for A if both firms engage in R&D?

Answer 1

The expected payoff for Firm A when both A and B engage in R&D is calculated using the probability of each firm's success and the resulting profits based on different market scenarios, subtracting the fixed R&D cost of A.

Step-by-step explanation:

The question asks us to calculate the expected payoff for Firm A (Apple) if both firms, A and B (Blackberry), engage in R&D for a new technology given the cost and expected profits for different outcomes. Since both firms are equally likely to succeed, we need to consider the probability p of either firm developing the technology successfully. We are given that the profits from the new technology are $15 million if one firm is alone in the market and $5 million each if both firms develop it. There are no variable costs, but there is a fixed R&D cost of $10 million for A and $15 million for B.

Let's use p as the probability of success in R&D for both firms. The expected profits for A are the sum of the probability-weighted outcomes:

• If A succeeds and B fails (p*(1-p)), A gets the full profit: p*(1-p)*$15 million.
• If A fails and B succeeds ((1-p)*p), A gets nothing: (1-p)*p*$0.
• If both succeed (p*p), they share the market: p*p*$5 million each.

The expected payoff for A is then: p*(1-p)*$15 million + (1-p)*p*$0 + p*p*$5 million - $10 million (subtracting the fixed cost of R&D).

This simplified becomes: (p - p^2)*$15 million + p^2*$5 million - $10 million, which represents the expected payoff for A if both firms engage in R&D.