If the demand function is P = 74 – Qå and the supply function is P = (Q, + 2)². Calculate the consumer's surplus and producer's surplus under the perfect competition.
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- if a competitive firm's marginal costs always increase with output then at the profit maximising output level, producer surplus isIf the demand function for a product is p = 9/(x + 1) and the supply function is p = 1 + 0.2x, find the consumer's surplus under pure competition. (Round your answer to the nearest cent.)Firm A and Firm B sell identical goods The total market demand is:Q(P) = 1,000-1.0P The inverse demand function is therefore: P(QM) = 10,000-10QM QM is total market production (i.e., combined production of firm’s A and B). That is: QM = QA + QB As a result, the inverse demand curve for each firm is: P(QA,QB) = 10,000-10QA-10QB The difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function: TCA(QA) = 5000QA TCB(QB) = 5000QB Using the demand function and the cost functions above, what is firm A’s profit function? Using the profit function above and assuming that firm B produces QB, calculate what firm A’s best response is to firm B’s decision to produce QB. (Note: Firm A’s best response should be a function of QB) Using the demand function and the cost functions above, what is firm B’s profit function? Using the profit function above and assuming that firm A…
- If in a pure competitive market the supply function is defined by Q=0.5P-0.5 whilst the demand function is represented by P+Q2-25=0.determine the magnitude of the consumer's surplus and producer's surplusConsider the following production function for a firm: y=(x1-1)(x2-1), if x1≥1 and x2≥1; and y=0, if either x1<1 or x2<1: Find the firms supply function and verify the law of supply.The supply function for a product is 2p − q − 60 = 0, while the demand function for the same product is (p + 20)(q + 10) = 8100. Find the market equilibrium point.
- A profit-maximizing firm produces a good using two inputs through the production function f(x1, x2) = (x1 + x2)0.5. Find the profit function π(p, w1, w2) and the supply function y(p, w1, w2)Suppose the (inverse) demand for a firm’s product is given by P = 10−2Q and the cost function is C(Q) = 2Q What is the profit-maximizing level of output and price for this firm?Say the the aggregate inverse demand function is D(Q) = 100 - Q, where Q = q1+q2. Both firms have the same cost c(q)=cq. Only firm q1 is allowed to participate. Therefore, q2 = 0. Find the function that maximizes welfare. What is the demand and price when welfare is maximized?
- (i) If the demand curve for a particular commodity is p = −0.09x + 51 and the total cost function C(x) = 1.32x2 + 11.7x + 101.4,where x is the level of production. Find: 1. All values of x for which production of the commodity is profitable.Consider a market (aggregate) inverse demand function: p = 20 – 2 q. Find the market price where the market revenue is maximized.You are the manager of a firm that sells its product in a competitive market with market (inverse) demand given by P = 50 − 0.5Q. The market equilibrium price is $50. Your firm's cost function is C = 40 + 5Q2. Your firm's marginal revenue is Multiple Choice MR(Q) = 50 − Q. indeterminable based on the information in the question. MR(Q) = 10Q. $50.
