ket price for a guitar tuner is $20 and the cost functions are: TC (9) = .01q² + .2q + 4950 MC (q) = .02q + .2 (a) Find the profit-maximizing quantity of guitar tuners produced by a firm in this market. (b) Calculate the profit each firm will earn in this market (c) Graphically depiet the firm's profit-maximization problem. (note: this doesn't need to be to scale but should accurately reflect the sign of the profit)
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- The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs MC ($) Quantity of Ear Buds 5 10 15 20 25 30 35 40 2.00 2.45 3.55 4.00 5.50 5.98 8.52 pairs ATC ($) 2.00 2.00 2.15 2.50 2.80 3.25 3.64 4.25 Check my work Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? b. At the profit-maximizing quantity, what is the total cost of producing ear buds? c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? d. Now assume the market price is $5.50 per pair, and Buddies produces the…|1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)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 table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 25 2.20 30 2.02 2.17 35 2.45 2.21 40 3.57 2.38 45 4.00 2.56 50 5.46 2.85 55 5.93 3.13 60 8.53 3.58 Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds?The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rentedA 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 table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 20 1.00 25 2.00 1.20 30 2.46 1.41 35 3.51 1.71 40 4.11 2.01 45 5.43 2.39 50 5.99 2.75 55 8.47 3.27The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a perfectly competitive firm that produces novelty ear buds in a competitive market. The market price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 10 3.5 15 3 20 2.44 2.86 25 3.56 3 30 4.02 3.17 35 5.48 3.5 40 5.98 3.81 45 8.49 4.33 Instructions: In part a, enter your answer as the closest given whole imber. a. If Buddies wants to maximize its profits, how many pairs of ear buds should it produce? pairs Instructions: In parts b-d, round your answers to 2 decimal places. b. At the profit-maximizing quantity, what is the total cost of producing ear buds? $ c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what is Buddies weekly profit? 2$Suppose that each firm in a competitive industry has the following identical costs: Total cost: TC = 25+0.25Q2,where Q is an individual firm’s quantity produced. The market demand curve for this product is as follow: Demand: P=60-0.095Q,where P is the price and Q is the total quantity of the good. Currently. (i) Identify each firm’s fixed cost, variable cost, and its marginal cost. (ii) Suppose that there are 10 firms in the market. Construct the market supply function in the short run. Determine the equilibrium price and quantity. (Hint: If each firm’s supply function is Qi= a+bP then the market supply Qm can be the aggregated supply at each price as Qm = Q1+Q2+Q3+...+Qi where Qi is each firm’s supply function.) (iii) Calculate each firm’s production quantity and profit (or loss) in the short run. Predict whether a firm will decide to leave or stay in the market as well as the long-run market equilibrium with free entry and exit.
- Suppose that each firm in a competitive industry has the following identical costs:Total cost: TC = 25+0.25Q2,where Q is an individual firm’s quantity produced.The market demand curve for this product is as follow:Demand: P=60-0.095Q,where P is the price and Q is the total quantity of the good. Currently. (i) Identify each firm’s fixed cost, variable cost, and its marginal cost.(ii) Suppose that there are 10 firms in the market. Construct the market supply function in the short run. Determine the equilibrium price and quantity. (Hint: If each firm’s supply function is Qi= a+bP then the market supply Qm can be the aggregated supply at each price as Qm = Q1+Q2+Q3+...+Qi where Qi is each firm’s supply function.)The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC АТС of Ear Buds ($) ($) 9.00 - 10 2.00 5.50 15 2.44 4.48 20 3.56 4.25 25 4.50 4.30 30 5.02 4.42 35 5.96 4.64 40 8.56 5.13 Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds? c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? 2$ d. Now assume the market price is $5.50 per pair, and Buddies produces the…2. A firm has a cost function of C = 1000+20Q + 1/10Q2 and has a demand function as shown in the graph below: 100 90 80 70 70 60 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 Quantity (Q) -P (demand) a) Estimate the firm's demand function. You may assume that the slope is a whole number, and the intercept is a multiple of 10. (1 mark) b) Find the firm's revenue function. You do not need to draw it. (2 marks) c) Find the marginal revenue function, and draw it on a copy of the graph. (3 marks) d) Find and draw the marginal cost function. (3 marks) e) Use your results from parts (c) and (d) to find the profit-maximising level of output. (3 marks) f) Find the market price at this level of output. (2 marks)