1. Consider a firm with the following cost and inverse demand functions. Cost($) 20 9 3 Cost Function 1 2 3 quantity Price($) 16 13 10 Inverse Demand 2 3 quantity (a) What are the average costs of producing 1, 2, and 3 units for this firm? (b) What are the marginal costs of producing first, second, and third units for this firm? (c) Does this firm enjoy either economies or diseconomies of scale? (d) What are the profits of producing 1, 2, and 3 units for this firm? (e) When does the firm maximize its profit? Select from producing 1, 2, and 3 units.
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- Price and cost (dollars per student) $150 120 88 76 72 ATC 40 - MC MR 24,000 30,000 36,000 Quantity of students enroiled 15,000 Your college decides to offer a psychology course as a MOOC that can be taken by students anywhere in the world, whether they are actually enrolled in your college or not. The demand and cost situation for the MOOC is shown in the figure. The faculty member who designed the course argues: "I think the course should be priced so that the maximum number of students enroll." Which price should this faculty member favor? O A. $0 В. $40 C. $88 D. $150Consider total cost and total revenue given in the following table: TABLE IN IMAGE Calculate profit for each quantity. How much should the firm produce to maximize profit?(ii) Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points betweenwhole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2½.) At what quantitydo these curves cross? How does this relate to your answer to part (a)?(iii) Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in along-run equilibrium? (8.75)A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?
- 7) What is total fixed cost at the profit-maximizing quantity?Suppose that total unit sales of iPhones and Android phones depends on both Apple’s and Google’s advertising expenditures: Google Advertise Don’t Apple Advertise 100, 100 120, 60 Don’t 60, 120 80, 80 To find the firm’s profits from the sales figures, assume that the price is $30, that the marginal cost is $20, and that the fixed cost of advertising is $300. (a) Fill in the profits in the following simultaneous-move game: Google Advertise Don’t Apple Advertise ? ? Don’t ? ? (b) What is the Nash equilibrium of the game? What strategies result in thehighest industry profits? Explain in words why the firms don’t choosethose strategies?(a) How much is total fixed cost? (b) At what output is the price elasticity of demand equal to -1? (c) At what outputs does the firm break even?
- (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з5. Demand functions are X-100-Px and Y=152-2Py Total Cost is C-6x2 + 4y2 +4xy + 110, Optimize the profit using two variable regular optimization formula.A 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
- On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.Principles of Microeconomics Name: Homework #3 Prof. R. Harris DUE: Wednesday, April 17, 2019 at the beginning of class - NO EXCEPTIONS. Please remember to show all work and please be neat. Please staple this if you print it on your own. 1. Consider the following table of numbers, which represents demand and cost conditions for a com firm. petitive TR 600 0 1 2 $o $400 600 $400 $240 600 $430 $670 $960 $1,350 $1,840 $2,440 $3,120 $3,910 $4,800 600 600 600 600 600 600 5 6 7 600 600 9 10 (a) Fill in the missing values (b) Use the information in the chart to determine what level of output the firm should produce. Explain your reasoning.The accompanying graph shows the short-run demand and cost situation for a price searcher in a market with low barriers to entry. Price (dollars) 24 10 V ATC The firm will receive $ MR Quantity/time The firm will maximize its profit at a quantity of▼ units. D Options: 6, 8, 9, or 10 After choosing the profit maximizing quantity, the firm will charge a price of in revenue at the profit-maximizing quantity. The total cost of production for this profit-maximizing quantity is $ The maximum profit the firm can earn in this situation is How will the situation change over time? Options: 6,8 10, or 24 per unit for this output. O Profits will attract rival firms into the market until the profit-maximizing price falls to the level of per-unit cost. O The market will adjust until the price charged by this firm no longer exceeds marginal cost at the profit-maximizing quantity. O This market is already in long-run equilibrium, and will not change throughout time. O Losses will induce firms to leave…