Define Q to be the level of output produced and sold, and assume that the company total cost function is TC = 20 + 5Q + Q<. The demand for the output has been estimated to be Q = 25 – P. Total revenue is TR = P*GQ. Find the profit-maximizing quantity of output. %3D
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- Ajax Cleaning Products is a medium-sized firm operating in an industry dominated by one large firm—Tile King. Ajax produces a multiheaded tunnel wall scrubber that is similar to a model produced by Tile King. Ajax decides to charge the same price as Tile King to avoid the possibility of a price war. The pnce charged by Tile King is $20,000. Ajax has the following short-run cost curve: TC=800,0005,000Q+100Q2 Compute the marginal cost curve for Ajax. Given Ajaxs pricing strategy, what is the marginal venue function for Ajax? Compute the profit-maximizing level of output for Ajax. Compute Ajaxs total dollar profits.Jamie Co. has a patented disinfectant to clean the kitchen of restaurants. The marketdemand for her patented disinfectant is Q = 1,000 – 0.2P. Jamie Co. has a totalcost function of C = 100,000 + 2,000Q + 10Q2.What is the profit-maximizing price and output level of Jamie Co.? Show yourworkings.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.
- demand curve, marginal revenue curve and total cost curve for a product are as shown respectively Qd = 400 -2P MR = 200 -Q TC = 10Q . What is the profit-maximising level of output? [1] 0 [2] 10 [3] 190 [4] 200 [5] 400Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to beMC=q+35 MR=560+22q−q2Where q is the quantity produced and the firm’s break-even is 5 units per weekYou are Required to1. determine the total cost and the total revenue function in terms of q.2. estimate the output at which profit is maximize3. calculate the maximum profitSuppose the marginal revenue of a perfectly competitve firm is $10 and its marginal cost is $18 at its current level of production, then the firm should Question 8 options: a) increase output b) decrease output c) not enter the market d) none of the above
- The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) =1/30 q2 − 12.85q + 20 + 400/q, where q is the firm's output. i. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?ii. Determine the level of output for which the firmᇱs profit is maximized.iii. What is the firm's maximum profit?The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 +400/q, where q is the firm's output. i. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?ii. Determine the level of output for which the firm's profit is maximized.iii. What is the firm's maximum profit?Demand equation of SL.ltd tiles is estimated as P = 8000 - 24Q. Find the marginal revenue when Q= 100.
- The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:Q = 120,000 - 10,00Pwhere Q is the quantity demanded per year and P is the price per lamp. The firm’s fixed costs are $12,000 and variable costs are $1.50 per lamp.a. Write an equation for the total revenue (TR) function in terms of Q.b. Specify the marginal revenue function.c. Write an equation for the total cost (TC) function in terms of Q.d. Specify the marginal cost function.e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are total profitsmaximized?What price will be charged? What are total profits at this output level?f. Check your answers in Part (e) by equating the marginal revenue and marginal cost functions, determined in Parts (b) and (d), and solving for Q.g. What model of market pricing behavior has been assumed in this problem?A local microbrewery has total costs of production given by the equation TC=500+10q+5q2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) Write the equations showing the brewery's average variable cost.1. Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750ml size is: q = 4000 − 250p and his total cost function is: C(q) = 500 + 0.2q (i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J's profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.