Suppose a firm with market power faces the following inverse demand function and marginal revenue function . The firm has a cost function and...

Suppose a firm with market power faces the following inverse demand function  and marginal revenue function . The firm has a cost function  and marginal cost function . Suppose the firm is contemplating investing $5 in R&D that, if successful, would change the demand function to , marginal revenue function to , cost function to , and marginal cost function to  in the next time period (t = 1). If the R&D project fails, the firm's demand and cost functions would not change. Find the minimum probability of success needed to convince the firm to invest in the innovation. Assume a discount rate of 10%.