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Given: Q = -0.0250 L3 + 1.5 L2
a) Derive the AP and MP equations
b) What is the level of Q where AP and MP of labor is maximum?
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- Given: Q = -0.0250 L3 + 1.5 L2 a) Derive the AP and MP equations (4 pts) b) What is the level of Q where AP and MP of labor is maximum? 2. The chief economist for Lanux Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per television and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 19 0.7360 39.428 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 191.93 54.65 3.512…Consider the following production function: x = f0.K) = A e°k where xis the output e is the labour input, kis the capital input, and A, bare positive constants. (a) Set up the cost minimization problem and solve for the first order conditions using the Lagrange Method. Let wbe the wage rate and rthe rental rate of capital. (b) Using your answer in (a), find how much labour and capital would the firm use to produce x outputs, given wage rate wand rental rate of capital ? what are these functions called? (e) Using your answer in (b), find the minimum cost it takes to produce xoutputs, What is this function called?Derive formulae for the marginal products of the three inputs in the produc- tion function Q = 40K03L0.3R04. %D
- Suppose a firm faces the following average and marginal products of labor: APL = 50 + 2L - 0.05L2 MPL = 50 + 4L - 0.15L2 At what value of labor does Stage III of production begin?Suppose a firm faces the following average and marginal products of labor: APL = 200 + 5L - 0.08L2 MPL = 200 + 10L - 0.24L2 At what value of labor does Stage II of production begin?i) Derive the output elasticity of labour for the following further alternative production function: InY = c + aK +BL ii) Suppose ß = 0.5 and other factors are fixed, explain the percentage change in output due to a unit change in labour.
- Suppose that a rock star gives concerts. The production function of the concert is the following: Q(C, A,G) = (C – 10)/ªAª/4G+/4 where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman and G represents hourly contribution of guitarist George.1) Suppose the prdduction function for widgets is given by: q= KL – 0.8K² – 0.2L?. a.) Suppose K=10, at what level of labor input does this AP1,reach a maximum and how many widgets are pIdduced at that point? At what level of labor input does MP1=0 and how many widgets are produced at that point? Graph the TP1, AP1 and MP1 curves. b.) Suppose capital inputs were increased to K=20. How would your answers to parts (a) change? c.) Does the widget production function exhibit constant, increasing, or decreasing retums to scale?You are a manager for a company that manufactures office furniture. To estimate the production function for a particular line of office chairs, you hired an economist to work with engineering and operations experts. The report from these experts indicates that the relevant production function is ? = 2?½?½ where K represents capital equipment and L is labour.Workers at the firm are paid a competitive wage of 120 cedis per day and chairs can be sold for 400 cedis each. a. Your company has already spent a total of 8,000 cedis on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. i. Is this firm operating in the short-run or in the long-run? Explain your choice. ii. what is your profit-maximizing level of output and labour usage? iii. What is your maximum profit?
- In the Cobb-Douglas production function (Q - aL³¹K²): O a. a and b b. the marginal product of labor (L) is equal to 1 O c. a and c d. if the amount of labor input (L) is increased by 1 percent, the output will incre e. the average product of labor (L) is equal to 32Suppose the production function for widgets is given by q=KL+6L²-0.1L³ where q represents the annual quantity of widgets produced, K represents annual capital input and L represents annual labor input. A) Suppose K=10. At what level of labor input does average product of labor reach a maxiumum? How many widgets are produced at that point? B) Again assuming that K=10, at what level of labor input does MPL=0? C)Determine and show whether the production process exhibits law of diminishing returns.Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.