For the production function Q=K0.210.3 and the budget 141 = 8K + 2L find the NEW LEVEL in the optimal employment of capital (K) after wages change by a factor of 0.7 while maintaining the same level of output.
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- The 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.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.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.
- Suppose that a certain factory output is given by the Cobb-Douglas production function ?(?, ?) = 60?^1/3?^2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory’s output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither.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.)In 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.
- A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labor is maximized? How many persons are employed if the marginal physical product of labor is maximized? What is the quantity of X when the average variable cost is minimized?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.)QUESTION 1 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).
- A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labour is maximized? How many persons are employed if the marginal physical product of labour is maximized? What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings. Assume that the price of x equals 1. a) Specify the utility maximization problem, write down the Lagrange function, and solve for the first order conditions. b) Solve for the MRS condition between consumption and hours of work. c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise. Explain (and either show mathematically or graphically) how this will affect the optimal number of hours of work of the person.For the production function Q budget 138 = 8K + 4L find the change in the optimal employment of L after wages change by a factor of 1.3. 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). = K0.7L0.6 and the
