A pharmaceutical manufacture (firm 1) currently has a patent for the only drug to treat a...

 

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A pharmaceutical manufacture (firm 1) currently has a patent for the only drug to treat a certain illness. The patent lasts one period. In period two, a second firm will be permitted to enter the market with a generic version of the drug. Producing the drug is tricky, but employees become more productive in the 1 1+ Qi manufacturing process with experience. In particular, the marginal cost of production at a firm i is where Q; is the firm's cumulative past output of the drug. Note that the marginal cost is decreasing in Q₁. In period 1, demand for the drug is given by the downward sloping demand curve q(p). In period 2, consumers will view the original drug and the generic (if any) as imperfect substitutes. When both the original and generic drugs are offered, each firm i’s demand is given by qi(Pi, P-i) = 10 − Pi + P-i, where p; and p_; are firm i's own price and opponent's price. If there is no entry by a generic producer, however, firm 1's demand curve is exactly as in period 1. Assume that there is no discounting between periods. (a) Suppose a generic manufacture (firm 2) does enter. Derive each firm's best response function in the period-2 price setting game. Provide a graphic illustration. Show how firm 1's best response function is affected by changes in Q₁. (b) How is firm 2's equilibrium profit affected by Q₁ (i.e., is it increasing or decreasing in Q₁)? [A careful qualitative argument is enough if you choose to do so.] (c) Suppose firm 1 wants to accommodate entry. How does the optimal period-1 production for firm 1 compare to the counterfactual case where the patent is in force for both periods (so that no entry is possible in period 2)? A pharmaceutical manufacture (firm 1) currently has a patent for the only drug to treat a certain illness. The patent lasts one period. In period two, a second firm will be permitted to enter the market with a generic version of the drug. Producing the drug is tricky, but employees become more productive in the 1 1+ Qi manufacturing process with experience. In particular, the marginal cost of production at a firm i is where Q; is the firm's cumulative past output of the drug. Note that the marginal cost is decreasing in Q₁. In period 1, demand for the drug is given by the downward sloping demand curve q(p). In period 2, consumers will view the original drug and the generic (if any) as imperfect substitutes. When both the original and generic drugs are offered, each firm i’s demand is given by qi(Pi, P-i) = 10 − Pi + P-i, where p; and p_; are firm i's own price and opponent's price. If there is no entry by a generic producer, however, firm 1's demand curve is exactly as in period 1. Assume that there is no discounting between periods. (a) Suppose a generic manufacture (firm 2) does enter. Derive each firm's best response function in the period-2 price setting game. Provide a graphic illustration. Show how firm 1's best response function is affected by changes in Q₁. (b) How is firm 2's equilibrium profit affected by Q₁ (i.e., is it increasing or decreasing in Q₁)? [A careful qualitative argument is enough if you choose to do so.] (c) Suppose firm 1 wants to accommodate entry. How does the optimal period-1 production for firm 1 compare to the counterfactual case where the patent is in force for both periods (so that no entry is possible in period 2)?

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