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1. Suppose a monopoly firm faces the following demand and marginal revenue functions: p = 200 – 2Q and MR = 200 – 4Q. The monopoly has a constant marginal cost of $40 and a fixed operating cost of $1000. Answer the following questions:
a. Calculate the size of the consumer surplus in this market.
b. Calculate the size of the producer surplus in this market.
c. Calculate the size of the monopoly deadweight loss in this market.
d. Suppose the firm is considering investing in R&D that, if successful, has 10% chance of reducing marginal cost to $20 in the next time period (t = 1) and 40% chance of reducing marginal cost to $30 in the next time period (t = 1). If it fails, the firm’s marginal cost stays at $40 in the next time period. The fixed operating cost is assumed not to be affected by the R&D investment. The R&D spending is considered to be a one-time fixed and sunk investment. Find the maximum amount of R&D spending the firm is willing to commit given the probabilities of success and the results of the process innovation. Assume a discount rate of 10%.
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