For the production function Q = K0.5L0.3 and the budget 143 = 6K + 5L find the optimal employment of L. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
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- 6. A company uses two inputs, unskilled labour (L) and capital (K), to produce itsproduct. The wage rate for a unit of labour is €5, while a unit of capital cost €20.a) Determine the equation and plot the isocost line for the company's expenditures on itsinputs of €1,000. Label the intercepts of the isocost with both axes. Draw a typical isoquantfor an output level Q0 and indicate the optimal input levels of L and K. (Do not forget tolabel the axes).b) Suppose the government introduces a minimum wage for unskilled labour of €6 per unit.Show graphically and explain shortly how much it would cost the firm in the short run,with capital input fixed at K, to keep its output constant at Q0.c) Show graphically and comment shortly on the optimal factor mix that the firm would useto produce Q0 in the long run at the specified minimum wage of €6 per unitThe output at a certain factory is Q(x, y) = 6x² + 3e*/36 VJ + 3y. where x and y denote, respectively, the number of hours of skilled and unskilled labor used. The current labor force consists of 35 hours of skilled labor and 49 hours of unskilled labor. Find the marginal rate of technical substitution. O Give your answer as a decimal accurate within +1% of the exact answer.A company produces children's toys. The manager noticed the connection between the number of employed workers and the quantity of toys produced per month, which are presented in the table of following: a) In what period is this firm operating? Why? b) What is the average product when 5 workers are employed? c) What is the marginal product when 7 workers are employed? What does this value mean? d) Does the law of declining marginal income apply? If yes to which worker? e) In this production function do we have total declining revenues? If so, which worker happens? f) Graph the curves of total product (TP), marginal product (MP) and product average (AP).
- The following data give the hourly wage rates (Rands) for a sample of 20 workers selected from a largecompany.12.50 9.45 13.85 7.25 8.70 14.60 11.75 14.50 10.80 12.457.50 15.90 9.75 11.50 13.30 6.25 15.50 12.80 5.35 9.50 (vi) Draw an OGIVE curve corresponding to the data and use it to estimate the median.Consider the housing construction industry. Assume that the industry is perfectly competitive in both input and output markets. Suppose that, through collective bargaining, a labor union negotiates an industry-wide wage for various kinds of labor (electricians, plumbers, and so on). In particular, it succeeds in negotiating a wage increase for carpenters from $15 to $20 per hour. The following graph shows the labor demand of an individual firm. On the following graph, show what happens at the firm level as a result of the union negotiations. WAGE RATE (Dollars per hour) 30 25 20 15 10 5 0 0 20 40 60 80 Demand Supply 100 120 QUANTITY OF LABOR (Number of workers) Now consider the effects of the wage change on the entire industry. Demand Supply ? Use the graph input tool to help you answer the following questions. You will not be graded on any changes you make to this graph. Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will…Please find the attached calculation question
- A breeder tells you he has determined for each 1-lb increase in weaning weight profit increases by $1.40 per pound. However, he has also calculated that for each independent 1-lb increase in birth weight, profit decreases $5.45 per pound. 1. What would be the economic index for this aggregate breeding value? 2. If the producer gave you the following table with calf birth weight and weaning weight, what would be the index value and rank for these animals? Calf id Weaning weight Birth weight Index value Rank 608 78 589 70 566 80 532 75 5. 556 76 618 87 7. 576 74 8. 610 88 9. 595 90 10 625 73 3 4 6Assume that quantities do not need to be integers. That is, it is feasible for Andreas to knit 37.5 mittens. You have two employees, Meb and Des, each of whom works for 10 hours a day. Meb can knit 5.2 mittens in an hour. Meb can knit 2 scarves in an hour. Des can knit 1.2 mittens in an hour. Des can knit 1 scarf in an hour. If they are efficiently knitting 18 scarves a day, what is the opportunity cost, in terms of mittens per day, of producing an extra scarf each day. Enter a number (and only a number, no units) rounded to two decimal places. If your answer is 1.275, enter 1.28. 2.6In a certain factory the production is Q = 120K1/2L1/3 units, where K represents the capital investment measured in units of $ 1,000 and L the size of the labor force measured in worker-hours. Currently, the capital investment is $ 250,000 and 400 worker-hours are employed. Apply the total differential of Q to estimate the resulting change in output, if the capital investment increases by $ 500 and labor increases by 2 hours-worker.
- Question 17 The average product of labour is the output per employee often in table 17.1 to answer the question below. Table 17.1 Output units 1000 2 500 6 000 7 000 8 000 C) d) Number of employees 10 20 30 50 As the number of employees increases from 10 to 50 the a) Is constant b) Falls then rises Rises FallsWhich of the following diagrams shows fixed proportion isoquants? A X1 X1 X2 X1 D X2 X1 O A OB OC2) Find the second order total differential, dz, of the function z = x?y?.