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Unformatted text preview: New Technology and Profits Another useful comparative statics exercise is to determine how much a firm would pay to reduce its marginal costs to that of its competitor. This will simply be the difference between its profits with the new, lower marginal cost and its profits before the investment. We would thus have to calculate equilibrium profits in the two equilibria. Therefore, this is different than what we did before in the sense that we will start with an asymmetric duopoly and examine a shift to a symmetric one. Recall with the differing technologies, we had differing marginal cost values c 1 , c 2 , and we solved for aggregate equilibrium output: Q N = 2 a- c 1- c 2 3 b New Technology and Profits Which we can sub into the demand function to get equilibrium price: p N = a + c 1 + c 2 3 With equilibrium price and quantity compute we can calculate equilibrium profits before investing in the new technology. Profits are ( p- c 1 ) q 1 . Which after plugging in our previous expression for equilibrium prices and quantities, we get (after some messy algebra): π 1 = 1 b a + c 2- 2 c 1 3 2 Recall what we are interested in is how much Firm 1 is willing to pay to lower its marginal cost to c 2 . New Technology and Profits...
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This note was uploaded on 10/15/2008 for the course ECON 188 taught by Professor Shakeebkhan during the Fall '08 term at Duke.
- Fall '08