1. The Zinger Company manufactures and sells a line of sewing machines. Demand per period (Q) for a particular model is given by the following relationship: Q= 400 - 5P where P is price. Total costs (including a "normal" return to the owners) of producing Qunits per period are: TC = 20,000 + 50Q + 3Q² (a) Express total profits (t) in terms of Q. (b) At what level of output are total profits maximized? What price will be charged? What are total profits at this output level? (c) What model of market pricing has been assumed in this problem? Justify your answer.
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- A company is planning to manufactureand market a new two-slice electric toaster. After conducting extensive market surveys, the research department provides the following estimates: a weekly demand of 200 toasters at a price of $16 per toaster and a weekly demandof 300 toasters at a price of $14 per toaster. The financial department estimates that weekly fixed costs will be $1,400and variable costs (cost per unit) will be $4. 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 functionin terms of ?. c)Determine the Marginal Revenu eat 2 different production levelsfor example 350 and 600 units. Interpret these results.(HINT: Consider what a positive or negative first derivative implies) d)Assume that the cost function is linear. Use the financialdepartment’s estimates to express the cost…. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.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…
- Revenue and Cost The total revenue function for LED TVs is given by R = 1050x dollars, and the total cost function for the TVs isC = 10,000 + 30x + x2dollars, where x is thenumber of TVs that are produced and sold.a. Which function is quadratic, and which is linear? b. Form the profit function for the TVs from thesetwo functions.c. Is the profit function a linear function, a quadraticfunction, or neither of these?When Apple introduced its first portable media player, the iPod, its constant marginal cost of producing the top-of-the-line model was $200 (iSuppli), its fixed cost was approximately $736 million, and we estimate that its inverse demand function was p = 600 - 25Q, where Q is units measured in millions. Be sure to express your answers in the proper units, where needed. a. What was Apple's average cost function? b. Assuming that Apple was maximizing its short-run monopoly profit, what was its marginal revenue function? c. What were its profit-maximizing price, quantity, profit and Lerner Index? d. What was the price elasticity of demandA profit-maximising firm in a competitive market is currently producing 1,000units of output. It has average revenue of $50, average total cost of $40 and fixed cost of $10,000.a) What is its profit?b) What is its marginal cost?c) What is its average variable cost? Is the efficient scale of the firm more than, less than or exactly 1,000 units?
- PakPerfect Inc. estimates equation of its total costs of production as TC = 500 + 10Q + 5Q2 and market demand for its product as Qd = 105 – (1/2) P, where Q is quantity in units and P is price in Pak$. a- Write the equations of the firm’s costs, as a function of Q: Average Total Cost ATC Average Variable Cost AVC Average Fixed Cost AFC b- Given above costs can you determine what will be the firm’s production in Stage 1? c- What is the breakeven price and breakeven quantity for this firm?PakPerfect Inc. estimates equation of its total costs of production as TC = 500 + 10Q + 5Q2 and market demand for its product as Qd = 105 – (1/2) P, where Q is quantity in units and P is price in Pak$. (i) Write the equations of the firm’s costs, as a function of Q (ii) Average Total Cost ATC (iii) Average Variable Cost AVC (iv) Average Fixed Cost AFC a. Given above costs can you determine what will be the firm’s production in Stage 1? What is the breakeven price and breakeven quantity for this firm? b. What is the shutdown price and quantity for this firm? c. Draw the firm’s costs in a graph as per your determination in (a). Label the breakeven and shutdown price and quantity using information in (b) and (c) above. d. Given the market price of Pak$ 50 (i) how many units should the firm produce? (ii) how many firms are competing in this market in short-run? (iii) How many firms will be in the industry in the long-run? e. How do you interpret the profit or loss condition of PakPerfect?…1. If profit is maximum at sales of 700 units, does the firm have no choice but to limit sales at this level? Explain your answer. 2. A business firm produces and sells a particular Variable cost is P30/unit. Selling price is P40 per unit. Fixed cost is P60,000. a. What is the break-even quantity and break-even point? Show your solution. 3. A manager makes the statement that output should be expanded as long as average revenue exceeds average Does this strategy make sense? Explain. 4. Suppose that the steel firm’s costs are shown below: Complete the table and determine the optimal output to be Price of steel P17 per unit. Output (Q) TFC TVC TC MC TR MR Profit/Loss 0 500 0 1 500 50 2 500 90 3 500 140 4 500 200 5 500 270 6 500 350 7 500 450…
- 1) A manufacturer of kitche. Appliances is preparing to set the price on a new blender. Demand is thought to depend on the proce qnd is represented by the following model. D= 2,800-4p The accounting department estimates that the total cost can be represented by the following model. C=4,700+5D Develop a mathematical model for the total profit of TP in terms of the price, P. A mathematical mod for the total profit in terms of the price P is TP= ______4. Assess which of the following is true and which is false.A firm’s profit equation is given by π = -100 + 160Q – 20Q2. Therefore,a) The firm’s fixed cost is 100.b) The firm’s fixed cost is 40 and variable cost is 20.c) Marginal profit is Mπ = 160 – 20Q.d) The firm’s profit-maximizing output is Q = 4.e) Marginal profit is Mπ = 160 – 40Q and it is positive for quantities that are lower than theprofit-maximizing quantity.for a firm with price in excess of average total cost, the presence of ecomonics profits implies that the firm should increase output in the short runeven if the price is below marginal cost . true or false explain