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Mathematics for Business and Economics
Q1) 3x2 ( 12x3 + 20 )0.5 within the range 6 and 8.
Q2)
The marginal revenue of a firm is given by the following equation: MR(Q) = 20 + 14Q + 13Q2
Where, Q represents the quantity produced.
Also given, the total revenue of the firm, when they produce 5 units of output, is 50, i.e., TR(5) = 50.
a)Calculate the firm's total revenue function. What is the value of the constant term in the total revenue function?
b)Calculate the total revenue of the firm when the firm produces 7 units of output.
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- A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.Give only typing answer with explanation and conclusion The market demand for a monopoly firm is estimated to be: Qd = 100,000 - 500P + 2M + 500PR where Qd is quantity demanded, P is price, M is income, and PR is the price of a related good. The manager has forecasted the values of M and PR will be $50,000 and $20, respectively, in 2016. The average variable cost function is estimated to be AVC = 520 - 0.03Q + 0.000001Q2 Total fixed cost in 2016 is expected to be $4 million. The profit-maximizing price for 2016 is $80. $100. $260. $520. $560.A production process varies only with raw materials, as all other inputs are fixed.The cost of a shipment of 8kg of raw materials is fixed at $85.It takes 5kg of raw materials to create one item of output, Q.The marginal revenue for this process is expressed by the equation: MR = -Q^2 + 52Q− 576.Determine the optimal amount of raw materials to be utilized in this production process.
- A manufacturer of mountain bikes has the following marginal cost function: C′(q)=700/0.5q+2 where qq is the quantity of bicycles produced. When calculating the marginal revenue and marginal profit in this problem, use the approach given for the marginal cost and marginal revenue in the discussions in your textbook. a) If the fixed cost in producing the bicycles is $3200, find the total cost to produce 35 bicycles.Answer: $ b) If the bikes are sold for $250 each, what is the profit (or loss) on the first 35 bikes?Answer: $ c) What is the marginal profit on bike number 36?Answer: $Given the following total revenue (TR) and total cost (TC) functions for a firm, write down the firm’s profit function. Determine the level of output the firm should produce in order to maximize profits by using the first-order condition. Confirm that this quantity represents maximum profits by using the second-order condition.TR=4000Q−33Q2TC=2Q3−3Q2 +400Q+5000Faye is an entrepreneur considering whether to enter the market for providing websites to universities offering online learning. The market is currently perfectly competitive, and the market-clearing price is $10,000 per client. Her marginal cost is given by the equation MC = 200Q. a. In this market, what is Faye’s marginal revenue function? b. If Faye enters the market, how many website clients will she have, and what will her profit be? You can assume no fixed cost. Now imagine Faye asks you for advice. She knows you have just taken this course, and you learned about market power. c. Explain two ways Faye can achieve greater market power in this market. Faye takes your advice, and she is now the monopolist in a new market, where the demand curve is given by Q = 300,000 – 1,000P d. What is Faye’s new marginal revenue curve? e. In this new market, how clients will she have, and at what price will she sell her services? Now imagine you see all the profits Faye is making and you decide…
- Q: Find the Marginal Revenue and Marginal Cost functions from the following equations 1. TR= Q3 – 6Q2 + 140Q + 750 2. TC= 35 + 5Q -2Q2 +2Q3Question 15 (i) Which of the following is(are) correct about how accountants and economists consider costs? Accountants consider only implicit costs Economists consider both explicit and implicit costs A: 1 only B: 2 only C: Both 1 and 2 D: Neither 1 nor 2 (ii) Which of the following statements is(are) correct for a monopoly firm and a competitive firm? Both firms earn economic profit in the long run. Both firms aim to maximize profit and produce at P = MC. A: 1 only B: 2 only C: Both 1 and 2 D: Neither 1 nor 2Consider a computer hardware production firm with total cost function TC = 2200+480Q+20Q2, and market demand function Qd = 190 – 2P; Q is output and P is market price. (a) Determine the firm’s Total Cost when it produces 120 units of output. (b) Determine the firm’s Marginal Cost when it produces 120 units of output. (c) Determine the firm’s Average Cost when it produces 120 units of output. (d) Find the market price of the firm’s output when it sells 120 units of output. (e) Determine whether the firm makes profit, or loss, at 120 units of output.
- Find the Marginal Revenue and Marginal Cost functions from the following equations TR= Q3 – 6Q2 + 140Q + 750 TC= 35 + 5Q -2Q2 +2Q3Suppose the revenue (in dollars) from the sale of x units of a product is given by R(x) = 56x2 + 65x 2x + 2 . Find the marginal revenue when 25 units are sold. (Round your answer to the nearest dollar.)$ Interpret your result. When 25 units are sold, the projected revenue from the sale of unit 26 would be $ .Suppose that the firm in a competitive market faces the following revenues and cost: Quantity Total Revenue Total Cost 0 $0 3 1 $7 5 2 14 8 3 21 12 4 28 17 5 35 23 6 42 30 7 49 38 In order to maximize profits, the firm will produce__ a. 6 units of output because marginal revenue equals marginal cost. b. 8 units of output because marginal revenue equals marginal cost. c. 4 units of output because marginal revenue exceeds marginal cost. d. 1 unit of output because marginal cost is maximized.
