QUESTION 1 A firm in a monopolistically competitive market faces the following demand curve: Q(P) = 21,984-687P Its total cost function is: C(Q) = $6675+24Q Calculate the profit maximizing quantity %3D
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- A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionComplete the following table showing the demand for snow skiing lessons per day. Do this by filling in the values for (i), (ii), and (ii). Average Revenue (AR = TR/Q) Marginal Revenue (MR = ATRIAQ) Lessons Total Revenue (TR =PxQ) Price (P) $70 per Day (Q) $65 55 45 1 65 65 60 55 50 45 $65 2 3 120 60 (i) 200 225 55 4 50 35 5 (ii) 40 25 6. 40 240 15 7 35 245 35 5 8 30 240 30 (ii) (i) Total revenue for 3 lessons is $ (ii) Average revenue for 5 lessons is S (iii) Marginal revenue for the 8th lesson is $What is the demand function and cost function based on the set of data below? Price Quantity Profit $50 88 -$240 $25 289 -$240 $80 -$2000 $52 148 $1256 $51 143 $1003 $55 103 $575
- |1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 10 + 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) %3D P'(x) (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue 2$ profit 2$ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.Suposse a munufacture of widgets has a fixcost of $2500, a variable cost of $30 per widget ans sell 100 widgets for 4,500. Find the cost function C(n) Find the revenue function R(n) Find the profit function P(n)
- Suppose a representative monopolistic firm faces the following demand function: Pi = 20-2qi where pi is the real price and qi is the (real) output. Assume the firm's total cost function is: Ci= 4qi (a) Derive the marginal revenue function and the marginal cost function, respectively. (b) Find the profit maximizing output and real price. (c) If the expected price, Pe = 2, what profit maximizing nominal price the firm would set? Explain.In a monopolistically competitive industry, a firm has a short-run and long-run cost function C = 150 + 20Q + 5Q2 The demand function for the firm's product is Q = α – P. (C = cost, Q = quantity, P = price, α = parameter). (i) If α = 116 short, determine the quantity, the price and profit of the business. (ii) What is the firm's demand function at long term equilibrium? MAKE A GRAPHComplete the following table showing the demand for snow skiing lessons per day. Do this by filling in the values for (i), (ii), and (iii). Average Revenue (AR = TR/Q) Marginal Revenue (MR = ATR/AQ) Lessons Total Revenue Price (P) (TR =P× Q) $0 per Day (Q) $90 $86 82 86 86 $86 82 164 78 (i) 296 3 78 78 70 74 74 62 70 350 (ii) 54 6 66 396 66 46 7 62 434 62 38 8 58 464 58 (iii) (i) Total revenue for 3 lessons is $. (ii) Average revenue for 5 lessons is $. (iii) Marginal revenue for the 8th lesson is $.
- A publisher has the following table of demand for the next novel by one of its famous authors: Price Number of novel in demand 100 0 90 1 80 2 70 3 60 4 50 5 40 6 30 7 20 8 10 9 0 10 The author is paid $2 to write the book (Fixed Cost or FC) and the marginal cost (MC) of publishing it is a constant $10 per book. a) Calculate the total revenue, total cost, and corresponding profits for each quantity. What quantity would a profit-maximizing publisher choose? What price would he set? b) Calculate marginal revenue. How does marginal revenue compare to price? Explain. c) Plot the marginal revenue (MR), marginal cost (MC), and demand (D) curves. At what quantity do the marginal revenue and marginal cost curves intersect? What does this mean? d) Obtain the economic profits (EP) of this monopolist and graph.Central Grocery in New Orleans is famous for its muffaletta, a large round sandwich filled with deli meats and topped with a tangy olive salad. Suppose the following table represents cost and revenue data for Central Grocery. Muffaletta Sold per Day Price (P) Total Revenue (TR) Marginal Revenue (MR) Total Cost (TC) Marginal Cost (MC) Average Total Cost (ATC) Profit 0 $15 $12 1 14 18 2 13 20 3 12 21 4 11 23 5 10 26 6 9 30 7 8 35 8 7 42 9 6 52 10 5 78 Fill in the table What are the profit-maximizing price and quantity, and what…The demand curse facing a firm in long run monopolistic competition is P= 350- Q. the firm's total cost is TC=355Q -2q2 + 0.05Q3 (355Q-2Q) what is the EQUAILİBRUM price? a) 240 b)300 c)340 d) None of the above
