1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C (Q1, Q2) = Q1+3Q²/ where Q₁ and Q₂ represent the output levels of product 1 and product 2. (e) Find the maximum proifit that this firm can earn as a function of P₁ and P₂.
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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.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.A price-taking firm in a competitive industry of a good that is continuously divisible (like sand) has a total cost function TC(Q) = 3.5Q^2 + 100Q + 500. The market price for the good is p = $240. a: Carefully write out this firm’s profit maximization problem, using the particulars of thisproblem. b: Give the marginal condition (equation) that characterizes the solution to this problem. Solvethis condition for the firm’s optimal quantity Q*. c: Calculate the firm’s maximized profit. d: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve andmarginal cost curve. Show Q* on your graph. e: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to totalrevenue and variable cost.
- c)Given that the cost function MC=x-2x^2-1 and the revenue function as MR=2x^2-3x-1.Assuming pure competition,determine the point atwhich profit maximized and the total profit made.If the demand function faced by a firm is:Q = 90 – 2PTC = 2 + 57Q – 8Q2 + Q3 Determine the best level of output for the above question by the MR and MCapproach.Question 2: Determine the best level of output for a perfectly competitive firm that sells its product at P = $4 and faces TC = 0.04Q3– 0.9Q2 + 10Q + 5. Will the firm produce this level ofoutput? Why? Question 3: Suppose that the production function is given as follows:TPL = 10L + 5L2 + L3Find the total product, Marginal product and average product when L = 5. Question 4: Find the optimum level of output and profit from the cost functionTC = 50 + 6Q2 and price P = 100 – 4QAlso derive marginal cost and marginal revenue.Start from a market with perfect competition. For a representative producer, the long-term marginal cost is given by LMC=9Q2−20Q+50LMC=9Q2−20Q+50 and the long-term total cost function is LTC=3Q3−10Q2+50QLTC=3Q3−10Q2+50Q Assume that the price on the market right now is SEK 50. a) How much profit or loss does the producer make in the initial situation? b) Describe in detail what will happen in the market and why c) What will the equilibrium price be? d) how much will our producer produce at market equilibrium?
- Suppose Glen’s Grinders, LLC is a retail outlet that sells meat grinders for household use and operates in a perfectly competitive market where there is a total of 10 firms in this market including Glen’s Grinders. Basically, all the firms in this competitive market have technologies (production and cost conditions) that are the same as Glen’s. Suppose Glen’s total cost function is given by: C(q) =100 + 25q + q^2 a. Calculate Glen’s optimal output level and profits if the monthly market inverse demand for units of the product is stable and given by: P= 250 - Q b. If Glen is typical of the firms in this industry (same as the other 9), calculate the long-run equilibrium output, price, and profit level that will ultimately prevail in this industry.Given - Answers for question #1 A-D (A)πA=780QA−145(QA+QB)QA−400QAπA=780QA-145QA+QBQA-400QA is the firm profit function of firm A . (B)QA=8550−QB2QA=8550-QB2is the best response function of firm A (C)πB=780QB−145(QA+QB)QB−260QBπB=780QB-145QA+QBQB-260QB is the firm profit function of firm B . (D)QB=11700−QA2QB=11700-QA2is the best response function of firm B Please answer questions #2 A-DSuppose that a perfectly competitive firm faces a market price of $7 per unit, and at this price the upward-sloping portion of the firm's marginal cost curve crosses its marginal revenue curveat an outpuut level of 1,400 units. If the firsm produces 1,400 units, it's average variable costs equal $6.50 per unit, and its average fixed costs equal $0.80 per unit. What is the firm's maximizing (or loss-minimizing output level? What is the amount of it's economic profits (or losses) at this output level?
- Sunrise Juice Company sells its output in a perfectly competitive market. The firm's total cost function is given in the following schedule: Output Total Cost (Units) ($) 0 50 10 120 20 170 30 210 40 260 50 330 60 430 Total costs include a "normal" return on the time (labor services) and capital that the owner has invested in the firm. The prevailing market price is $7 per unit. (a) Prepare (i) marginal cost and (ii) average total cost schedules for the firm. (b) What is the firm's profit maximizing output level? (c) Is the industry in long-run equilibrium? Justify your answer.The fact that a purely competitive firm’s totalrevenue curve is linear and upsloping to the right impliesthat: A. product price increases as outputincreases. B. product price decreases as outputincreases. C. product price is constant al all levels ofoutput. D. marginal revenue declines as more output isproduced.he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
