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04 final 12 - MRA = 6.5 — 0.1QA Setting MRA = MCA = 3 for...

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Unformatted text preview: MRA = 6.5 — 0.1QA Setting MRA = MCA = 3 for firm A’s profit maximiution yields 6.5 — 0.1QA = 3 or QA = 35 Substituting the value of QA into reaction function of firm B, Q; = 35 — 0.5QA= 17.5 Substituting the value of Q (=QA + Q3) into demand equation, P =10 - 0.1(35 + 17.5) = $ 4.75 The required increase in firm B’s FC, F5, to ensure that it would choose not to enter is given by Rg—VCE—(FCB+FB)<0 or (4.75 ~ 3)(17.5) — 15 - FE < 0 or F9 > $ 15.625 Question 15: Consider the following market for inventions. There are 1101 inventors, each of which owns the rights to one invention. The value of the inventions, if undertaken by firms, is uniformly distributed between -100 and 1000. That is, one invention would result in net income of -100 dollars if undertaken by a firm; another invention would result in net income of -99 dollars if undertaken by a firm; all the way up to net income of 1000 dollars. Each inventor knows the value of her own invention. Each inventor could develop her invention herself, but doing so would involve additional costs of 300 dollars, since the inventor is not really set up for production. There is an unlimited number of firms available to buy a project at a price equal to the value (the net income) expected from the invention. (3 points) a. If firms can identify the value of each invention, what will be the total quantity of inventions sold? All inventions from 0 to 1000: i.e. 1000 (or 1001, counting the 0'II value inventions) inventions. (6 points) b. If firms cannot identify the quality of the inventions before buying them, but know the distribution of the value of inventions, then: i. What price are firms willing to pay for inventions? ii. Which inventions will be sold and developed by firms? iii. Which inventions will be developed by the inventors themselves? The price P for inventions will attract supply from all inventions with value v between v=-100andv=P+300. The average value of these inventions = ( -100 + P + 300 ) /2. This average value must equal P in equilibrium: P = ( -100 + P + 300 ) [2 which yields (i) P = 200. So (ii) all projects with value [-100, 500] are sold ; (iii) all better projects (500, 1000] are developed by the inventors. 13 ...
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