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- A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…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 functionA manufacturer knows that: His TR is given by Revenue = 23Q – Q2 His total cost of production is; Cost = 36 + 2Q + 0.1Q2 Where Q is the weekly production in thousands a) Economists define MR as the rate of change of Total revenue. Derive an expression for Marginal Revenue (MR) b) How do you think Economists’ would define ‘Marginal Cost’? Derive an expression for marginal Cost (MC) c) What output will make marginal Revenue equal Marginal cost?
- 100 90 80 70 60 ATC 50 40 30 20 AVC МС О 10 + 0 0 5 10 15 20 30 35 40 45 50 QUANTITY (Thousands of shirts) or each price in the following table, use the graph to determine the number of shirts this firm would produce in order to maximize its profit. Assume hat when the price is exactly equal to the average variable cost, the firm is indifferent between producing zero shirts and the profit-maximizing uantity. Also, indicate whether the firm will produce, shut down, or be indifferent between the two in the short run. Lastly, determine whether it will nake a profit, suffer a loss, or break even at each price. Price Quantity (Dollars per shirt) (Shirts) Profit or Loss? Produce or Shut Down? Shut down 10 20,000 Loss Shut down 20 10,000 Loss Shut down 32 5,000 Loss Either 0 or 37,500 Shut down 40 Loss 25 COSTS (Dollars)Price and cost (dollars per student) $150 120 88 76 72 ATC 40 - MC MR 24,000 30,000 36,000 Quantity of students enroiled 15,000 Your college decides to offer a psychology course as a MOOC that can be taken by students anywhere in the world, whether they are actually enrolled in your college or not. The demand and cost situation for the MOOC is shown in the figure. The faculty member who designed the course argues: "I think the course should be priced so that the maximum number of students enroll." Which price should this faculty member favor? O A. $0 В. $40 C. $88 D. $150|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.)
- A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. ) If production increases continuously, what is likely to be the average cost per sink? How many laundry sinks will the company need to produce in order to maximise it′s profits? What is the maximum profit?A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. (a) Draw a large graph showing the Royal Mail’s average cost curve and itsmarginal cost curve. Show how many deliveries would be made, and at whatprice, if Royal Mail operated as a monopoly. Show the Royal Mail’s profit orloss on the graph.
- For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. (a) Draw a large graph showing the Royal Mail’s average cost curve and itsmarginal cost curve. Show how many deliveries would be made, and at whatprice, if Royal Mail operated as a monopoly. Show the Royal Mail’s profit orloss on the graph. (b) The government makes a law restricting the price of postage to £1. Show theeffect of this policy in the…For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. New technology changes delivery firms’ technology. Now, the minimumaverage cost is £2 at 1 million deliveries and a minimum marginal cost of £1at 0.75 million deliveries. The government removes all price restrictions andallows free entry. Describe the long-term outcome for this market, using twographs, one at the firm-level and one at the…For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. The government makes a law restricting the price of postage to £1. Show theeffect of this policy in the short-run in a new, large graph. The graph shouldshow the firm’s average cost, marginal cost, marginal revenue, and consumerdemand. How much postage is bought? Show on your graph if the Royal Mailis in profit or loss, and by how much.