A firm with market power faces the following estimated demand and average variable cost functions: Qd = 39,000 - 500P + 0.4M - 8,000PR AVC= 30 -0.005Q + 0.000000502 where Qd is quantity demanded, P is price, M is income, and PR is the price of a related good. The firm expects income to be $40,000 and PR to be $2. Total fixed cost is $100,000. What is the firm's profit? A. $220,000 B. $147,000
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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…The BCY Corporation provides accounting services to a wide variety of customers, most ofwhom have had a business association with BCY for more than five years.BCY's demand is: P = 24,000 – 20Q, and BCY's marginal cost of service is: MC = 40Q.a. If BCY charges a uniform price for a unit of accounting service, Q, what price must itcharge per unit, and how many units must it produce per time period in order to maximizeprofit? Calculate the consumer surplus.b. If BCY could enforce first-degree price discrimination, what would be the lowest pricethat it would charge and how many units would it produce per time period?c. With perfect price discrimination and ignoring any fixed cost, what is total profit andwhat is the amount of consumer surplus?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 function
- The accompanying graph shows the short-run demand and cost situation for a price searcher in a market with low barriers to entry. Price (dollars) 24 10 V ATC The firm will receive $ MR Quantity/time The firm will maximize its profit at a quantity of▼ units. D Options: 6, 8, 9, or 10 After choosing the profit maximizing quantity, the firm will charge a price of in revenue at the profit-maximizing quantity. The total cost of production for this profit-maximizing quantity is $ The maximum profit the firm can earn in this situation is How will the situation change over time? Options: 6,8 10, or 24 per unit for this output. O Profits will attract rival firms into the market until the profit-maximizing price falls to the level of per-unit cost. O The market will adjust until the price charged by this firm no longer exceeds marginal cost at the profit-maximizing quantity. O This market is already in long-run equilibrium, and will not change throughout time. O Losses will induce firms to leave…(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..nou Given cost and price (demand) functions C(g) = 110g + 43,000 and p(g) = - 1.8q + 890, what price maximizes revenue? len It would be $ per item. (Round answer to two decimal places.) llab lome Quiz Grade Study Goody
- (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem зAn industry currently has 100 firms, each of whichhas fixed cost of $16 and average variable cost asfollows:Quantity Average Variable Cost1 $12 23 34 45 56 6a. Compute a firm’s marginal cost and average totalcost for each quantity from 1 to 6.b. The equilibrium price is currently $10. How muchdoes each firm produce? What is the total quantitysupplied in the market?c. In the long run, firms can enter and exit themarket, and all entrants have the same costs asabove. As this market makes the transition to itslong-run equilibrium, will the price rise or fall?Will the quantity demanded rise or fall? Will thequantity supplied by each firm rise or fall? Explainyour answers.d. Graph the long-run supply curve for this market,with specific numbers on the axes as relevant.A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
- 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?A 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?