The inverse market demant curve for a duopoly market is p=14-Q=14-qi-q2, where Q is the market output, and q1 and q2 are the outputs of firms 1 and 2, respectively. Each firm has a constant marginal cost of 2 and a fixed cost of 4. Consequently, the Nash Cournot best response curve for Firm 1 is q1=6-q2/2.Create a spreadheet with columns titled q2, BR1,Q, p and Profit1. I nthe first column, list possible quantities for firm 2, q2, ranging from 0 to12 in increments of 2. The column headed BR1 shows the proft-maximizing output (best response) for Firm 1 given Firm2's output in the first column. The Q column sums the values in q2 and BR1 columns. The p column lists the price that corresponds to Q. The Profit1 column shows the profit of Firm 1, taking account its marginal and fixed costs. After filling in the spreadsheet, use a scatterplot option in Excel to draw the best-response curve for Firm 1.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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