For the production function Q = K0.7L0.4 and the budget 146 = 7K+ 4L find the change in the optimal employment of L after wages change by a factor of 1.7. 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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- F (L, K) = L0.2K0.7， The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. Derive the equation of the isoquant for y = 2 (with K in the vertical axis and L in the horizontal axis). Use the first and second derivative to show that this curve is decreasing and convex. Provide a graphical representation of the isoquant indicating at least one combination of labour and capital in this curve.Consider the following production function: 9=100L0.8K0.4 Currently the wage rate (w) is $4.00 and the price of capital (r) is $2.00. If the firm is using 200 units of capital in production, how much labor should be employed to minimize costs? Labor input = units. (Enter a numeric response using a real number rounded to two decimal places.)Suppose the two factors are perfect complements and the production function is given by y=min { 13x1,2x2} Where x1=300, X2=50 What will be level of production and draw corresponding iso quant?
- Suppose that a furniture manufacturer produces tables. The manufacturer's production function is Q(KL)- 2K0.8 0.2 where Kis the number of wood saws and L is the number of labor hours used to produce tables. The prevailing wage rate is $10 per hour and the rental rate associated with wood saws is $50. The manufacturer has a goal to produce 1,000 units. What Lagrangian equation can be used to solve the manufacturer's cost minimization problem? Oa. C = 2K12 s.t. 1,000 = 50K + 10L b. = Oc L = Od. L = 10K + 50L s. t. 1,000 = 2K08102 50K + 10L s.t. 1,000= 2KL02 2K10 s. t. 1,000= 10K + 50LOne employee of a computer store is paid a base salary of $4000 a month plus an 8% commission on all sales over $6000 during the month. How much must the employee sell in one month to earn a total of $5000 for the month? Write an equation required to find the solution, using x to represent the amount of sales, in dollars, by the employee. 8 4.000 + x+100 (Use integers or decimals for any numbers in the equation. Do not simplify.)0.25 0.75 q=LK The wage rate (w) is $10 and the rental rate Suppose that a firm had a production function given by: (r) is $5. Calculate the amount of labor the firm would hire when it produces 400 units of output in a cost-minimizing way. (Round to the nearest 2 decimal places if necessary.) Answer:
- Consider the following production function: Assume capital is fixed at K = 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when L= q=48LK+20L2 3 (3) ₁³. (Enter a numeric response using an integer.)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?A car wash firm calculates that its daily production (in numbers of cars washed) depends on the number of n workers it employs according to the formula P=30n-0.05n^2 cars. (a) Calculate the marginal product of labor at employment level of 50 workers. ___ cars/workers. Interpret the results. This means that, at an employment level of 50 workers, the firm’s daily production will increase at a rate of ____ cars per additional worker it hires.
- Consider the following production function: q= 100L0.8K0.4 Currently the wage rate (w) is $15.00 and the price of capital (r) is $5.00. If the firm is using 200 units of capital in production, how much labor should be employed to minimize costs? Labor input= units. (Entera numeric response using a real number rounded to two decimal places.)A Firm's Optimization with CES Production Function The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substitution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(Kt, Nt) = [aK{ + (1 − a)N]¹º 0A farmer uses a certain technology that produces electricity. His production function is given as: q = f (k, l) = 1000k¹⁰/20 – 201³ Where q is the no. of megawatts of electricity his company is producing. Suppose that their electrical generators, k=20, calculate for the following: 1. Marginal product of labor 2. Average product of labor if k=20 3. If k decreases from 20 to 17, calculate the new MP of labor and the average product. Explain intuitively what happens to the MP and the average product.SEE MORE QUESTIONS