Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of given by C = 400+2q² where q is the level of output and C is total cost. (The marginal cost of production, MC(q), is 4q; the fixed cost, FC, is $400) If the price of a watch is $120, how many watches should you produce to maximize profits?
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- You produce widgets. Currently you produce four widgets at a total cost of $40. What is your average total cost? Suppose you could produce one more (the fifth) widget at a marginal cost of $5. If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why? Suppose instead that you could produce one more (the fifth) widget at a marginal cost of $20. If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why?The cost of renting tuxes for the Choral Society's formal is $21 down, plus $87 per tux. Express the cost C as a function of x, the number of tuxedos rented. C(x) = Use your function to answer the following questions. (a) What is the cost of renting two tuxes? %$4 (b) What is the cost of the second tux? $4 (c) What is the cost of the 4,098th tux? 2$ (d) What is the variable cost? %24 What is the fixed cost? $4 What is the marginal cost? %24Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.
- 7. Assume that the marginal cost curve is given by mc(q) = 100 + 2q. (a) If the price is $160, what is the optimal production for the firm? What if the price is $120? (ignore the shut-down decision for this part) (b) Assuming that the market is cleared at $160 (no shortage/surplus). If the market demand is equal to 10,000 units of the product. How many firms are currently operating (n) in the market? (Hint: if the market clears qª = n x q°) (c) If the total cost curve is TC 256 + 100g + q², what's the average total cost curve? %3| what's the break-even price? (d) If the demand curve is given by qd = 8, 452 – p, what's the long-run equilibrium price, the equilibrium quantity and the long-run total number of firms (n) in the industry?A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³ -0.3x² +600x-800. Currently the company builds and sells 7 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 6 laptops weekly? c) What is the marginal profit when x = 7? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 8 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed) b) The decrease in profit is $ (Round to the nearest cent as needed.) c) The marginal profit when x=7 is $ (Round to the nearest cent as needed) CLOT d) The profit resulting from the production and sale of 8 laptops weekly is approximately $ (Round to the nearest cent as needed)VI. | Suppose the cost of producing milkshakes is C = Q³/3-30² +150 +50. What is the equation for marginal cost? At what point is marginal cost minimized?
- 6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of production is given by C= 300 + 29°, where q is the level of output and C is total cost. (The marginal cost of production, MC(q), is 4q; the fixed cost, FC, is $300). If the price of a watch is $80, how many watches should you produce to maximize profits? You should produce watches. (Enter your response as an integer.) What will the profit level be? Profit will be $ (Enter your response rounded to two decimal places.) At what minimum price will the firm produce a positive output? In the short run, the firm will produce if price is greater than $ per watch. (Enter your response as an integer.)Ebba Kantzen says the following: "I am currently producing 10,000 pizzas per month at a total cost of $50,000. If I produce 10,001 pizzas, my total cost will rise to $50,011. Therefore, my marginal cost of producing pizzas must be increasing." ( 1.) Using the point drawing tool, indicate the point of marginal cost. Label this point "Marginal cost." 2.) Using the point drawing tool, indicate the point of average total cost. Label this point "Average total cost." Carefully follow the instructions above, and only draw the required objects. Costs(dollars per pizza) (5.95,0) MC Quantity (pizzas per month) points ATC
- 13. The marginal profit for the new X-99 pogo stick is P'(x) = -0.1x+ 60 where x is the number of sticks produced and sold. The profit is - $1000 when 50 sticks have been produce and sold. a) Find the profit function. b) What level of production of pogo sticks (x) produces a maximum profit?2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changingSuppose a firm is currently maximizing profit by producing 100 units of output per day. It is then discovered that the firm owes $1,000 for a one-time tax violation that occurred a few years ago. The firm now needs to pay the $1,000 to the government no matter what. How should the firm react to this additional cost? The firm should increase output in order to increase revenue enough to cover the additional cost. The firm should continue to produce 100 units of output per day, as the $1,000 is a sunk cost and therefore has no effect on production decisions. The firm should shut down in the short run and start back up in the long run. The firm should decrease output in order to decrease variable costs by $1,000.