) A purely competitive firm has a single variable input L (labor), with the wage rate W, per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P. a) Write the production function, revenue function, cost function, and profit function of the firm b) What is the first-order condition for profit maximization? Give this condition an economic interpretation c) What economic circumstances would ensure that profit is maximized rather than minimized?
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- 1. Figure 1 shows the production function of a firm. Y В Y2 Y1 X X1 X2 a) What are the variables along (i) of the X axis? (ii) Y axis? b) Does the firm operate in the short term or long term? c) Referring to the diagram above, what is the level of input where (i) firms experiencing increased marginal output? (i) does the firm experience a declining marginal output? (i) the firm achieves maximum marginal output? (iv) the firm achieves a blank marginal output?1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?
- 8. siuppose that the manager of a firm operating in a competitive market has estimated the firm's average variable cost function to be: AVC= 18-0.3Q Total fixed cost is $60 and the forecasted price of the firm's product is $12. 79 a. What is the corresponding marginal cost function? b. At what output is AVC at its minimum? C. How much outputs should the firm produce? d. How much profit or loss will the firm earn?,1.Suppose a chair manufacturer is producing in the short run (with its existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:Number of Workers Number ofChairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to becomenegative.2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl
- 1. Suppose marginal cost and average cost are given by the following expressions: MC(x)=3x1/2, AC(x)=2x1/2. What is the profit maximising quantity when p=$3?2. Suppose marginal cost and average cost are given by the following expressions: MC(x)=3x1/2, AC(x)=2x1/2. What is the value pf the long-run break-even price?3. For any given level of the price of output, the supply curve of a producer tells the producer the amount of output to produce in order to maximise profits a. True b. False3. Suppose you are the new Manager of Kramerica Korporation, a firm which makes large rubber bladders for oil tankers with two inputs, capital and labor. On your first day, you discover that the marginal product of capital is 1,500, the price of capital (rent) is $100, the marginal product of labor is 500 and the price of labor (the wage rate) is $50. Based on these numbers, a. Is Kramerica employing its two inputs optimally? Explain your answer. b. What would you do as the new Manager, and why? Be specific!3. The "Sad Student" Company finds that it costs a total of C(q) = 9720 +500q – 1.5q +0.005q Dollars to produce q lots of its latest board game named "Calculus Teacher Shooter", each lot consisting of 100 games.. Analyze the behavior Interpret the effect of the of the marginal cost as a function of the output q constant term in the expression of total cost function on marginal cost function
- 1. The total cost of producing a quantity q is C(q). The average cost a(q) is given in figure below. The following rule is used by economists to determine the marginal cost C'(q0), for any qo: Construct the tangent line ti to a(q) at qo. Let t, be the line with the same vertical intercept as t, but with twice the slope of t, . Then C'(q0), is the vertical distance shown in figure below. Explain why this rule works. $/unit a(q) t2 t1 C'(qo)3) Which of the following is not true about the marginal cost? Oo The marginal cost (MC) curve is U shaped. It can be calculated by dividing the change in the total cost by the change in the output. It is the additional cost incurred by a firm from changing output by a certain amount. It can be calculated by dividing the total cost by the quantity.13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³ K+z! Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.