ESSEC Business School_ECOI 31143: Business Economics Final Exam. Questions & Solutions.

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ESSEC Business School_ECOI 31143: Business Economics Final Exam. Questions & Solutions. Consider a firm that owns a patent and hence monopoly rights for the production and distribution of a product. ... The inverse market demand for the product is given by p = 100 − 2q, where p is the price (i.e., WTP) and q is the quantity. The cost of producing q units of the product is given by c(q) = q2 + 40q + 25. 1. Write down the monopolist’s profit from producing q units of the product. (1p) Answer. Π(q) = pq − c(q) = (100 − 2q)q − (q2 + 40q + 25) = −3q2 + 60q − 25 2. Find the marginal revenue and the marginal cost of the monopolist when producing q units of the product. Using the marginal revenue and marginal cost, find the quantity that maximises the monopolist’s profits. Find also the price that maximises the monopolist’s profits. (1.5p) Answer. MR = 100 − 4q page 1 of 11Business Economics Final Exam Fall 2020 MC = 2q + 40 Profit maximisation condition: MR = MC , 100 − 4q = 2q + 40 , qm = 10 pm = 100 − 2qm = 100 − 20 = 80 3. Find the monopolist’s maximum profit and the consumer surplus when the monopolist charges its profit-maximising price. (1.5p) Answer. Πm = pmqm − c(qm) = 80 × 10 − (102 + 40 × 10 + 25) = 800 − 525 = 275 CSm = 1 2 (100 − 80)10 = 100 4. Find the Lerner index and own-price elasticity of demand when the monopolist charges its profit-maximising price. (1p) Answer. L = pm − MC(qm) pm = 80 − (2 × 10 + 40) 80 = 80 − 60 80 = 1 4 We know that L = −1 " , " = −4 5. Depict carefully in a diagram, in which the horizontal axis represents the quantity (q) and the vertical axis the price (p), the inverse demand, marginal revenue the marginal cost, the profit-maximising price and quantity and the consumer surplus. [Hint: Use a ruler and try as much as possible to locate all the numbers correctly. Do not forget the intercepts of the lines.] (1p) Answer. ESSEC Business School page 2 of 11Business Economics Final Exam Fall 2020 p 0 q 100 50 MR 80 10 20 MC CS p = 100 − 2q Suppose now that everything is as described above but the patent expires; hence, any firm can enter the industry and produce the product at a cost given by c(q) = q2 + 40q + 25. Therefore, the market after the patent expires becomes perfectly competitive (i.e., all firms are price-takers) and all firms are symmetric. 6. Write down a (representative) firm’s profit from producing q units of the product. [Hint: Recall that in a perfectly competitive market, all firms are price takers.] (0.5p) Answer. In this case, the price of the product is independent of the action of any of the firms (i.e., firms are price takers). Therefore, a firm’s profit is written as: Π(q) = pq − c(q) = pq − (q2 + 40q + 25) 7. Find a (representative) firm’s Minimum Efficient Scale (i.e., the output that minimises the average cost of production). Find the minimum average cost of production. (0.5p) Answer. We can find the MES either by minimising the AC or by equating the AC to the MC (because we know that the MC crosses the AC at the minimum AC. [Show More]

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