Two firms are in competition, producing a device that embeds a wireless microphone and speaker into...

 

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Two firms are in competition, producing a device that embeds a wireless microphone and speaker into a N-95 mask so that individuals wearing masks can still be heard clearly. The price-demand relationship for this device is P = 100-91-92, where q; indicates the quantity produced by firm i. Each firm initially has production costs ci(qi) = 20qi, but Firm 1 has the opportunity to hire a smart Purdue industrial engineering grad to reduce their costs. If the firm hires them at a wage of w > 0, the cost of production for Firm 1 would drop to C₁ (9₁) = 10q₁. Firm 2 does not have the same connections to Purdue, so they do not have this chance to improve their processes. This can be modeled as a dynamic game in which Firm 1 chooses whether or not to hire a Purdue grad, and then in the next stage of the game, both firms simultaneously choose what quantities qi to produce. Clearly, Firm 1 must weigh the wage w against the reduced marginal costs that would make them more competitive, deciding whether their total profits would be higher with or without the hire. What is the maximum wage w Firm 1 would be willing to pay for the reduction in their marginal costs? Assume that Firm 1's decision whether to hire the Purdue grad is common knowledge; in other words, both firms know if a Purdue grad has been hired to provide process improvements. (10 points) *s question is a continuation of Question 3, so consider the same basic setup with respect to the demand curve, production costs, etc. The only difference is whether Firm 2 knows about Firm 1's decision in the first stage of the game. a) Suppose that Firm 2 does not know whether Firm 1 has hired a Purdue grad to reduce their marginal costs, and Firm 2 has little insight into how much it would cost to hire a Purdue grad. They believe there is a 1/3 probability that Firm 1 has made the hire. Explain why this change makes the game equivalent to a static game of incomplete information. (2 points) b) Compared to their choice in Question 3, would Firm 2 increase their production, decrease it, or keep it the same? For this question, only a verbal argument explaining your intuition is required for full credit; no math is necessary. (2 points) c) Given this incomplete information setup, what are both firms' production decisions, and both firms' profits, if Firm 1 does hire a Purdue grad at a wage of w = 200? (6 points) Two firms are in competition, producing a device that embeds a wireless microphone and speaker into a N-95 mask so that individuals wearing masks can still be heard clearly. The price-demand relationship for this device is P = 100-91-92, where q; indicates the quantity produced by firm i. Each firm initially has production costs ci(qi) = 20qi, but Firm 1 has the opportunity to hire a smart Purdue industrial engineering grad to reduce their costs. If the firm hires them at a wage of w > 0, the cost of production for Firm 1 would drop to C₁ (9₁) = 10q₁. Firm 2 does not have the same connections to Purdue, so they do not have this chance to improve their processes. This can be modeled as a dynamic game in which Firm 1 chooses whether or not to hire a Purdue grad, and then in the next stage of the game, both firms simultaneously choose what quantities qi to produce. Clearly, Firm 1 must weigh the wage w against the reduced marginal costs that would make them more competitive, deciding whether their total profits would be higher with or without the hire. What is the maximum wage w Firm 1 would be willing to pay for the reduction in their marginal costs? Assume that Firm 1's decision whether to hire the Purdue grad is common knowledge; in other words, both firms know if a Purdue grad has been hired to provide process improvements. (10 points) *s question is a continuation of Question 3, so consider the same basic setup with respect to the demand curve, production costs, etc. The only difference is whether Firm 2 knows about Firm 1's decision in the first stage of the game. a) Suppose that Firm 2 does not know whether Firm 1 has hired a Purdue grad to reduce their marginal costs, and Firm 2 has little insight into how much it would cost to hire a Purdue grad. They believe there is a 1/3 probability that Firm 1 has made the hire. Explain why this change makes the game equivalent to a static game of incomplete information. (2 points) b) Compared to their choice in Question 3, would Firm 2 increase their production, decrease it, or keep it the same? For this question, only a verbal argument explaining your intuition is required for full credit; no math is necessary. (2 points) c) Given this incomplete information setup, what are both firms' production decisions, and both firms' profits, if Firm 1 does hire a Purdue grad at a wage of w = 200? (6 points)

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a In the case that Firm 2 does not know whether Firm 1 has hired a Purdue grad t... View the full answer