A cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?

a. A firm's long-run total cost can be written as LTC = 3000Q - 50Q2 + (1/3)Q3 and its long-run marginal cost by LMC = 3000 - 100Q + Q2. Find the range over which the firm will experience economies of scale. Explain your answer. b. A firm has a production function of Q = K * L + L, where the marginal product of labor is  MPL = K + 1 and the marginal product of capital is MPK = L. The wage rate (W) is $100 per worker and the rental price (R) is $100 per unit of capital. In the short-run, capital (K) is fixed at 4. Find the minimum total cost of production in the short- and long-run if the firm produces 100 units of output.

The production function is Q = f (L, K0). Explain the total product, the average product and the marginal product, show the curves also graphically

The equation below is a production function,   Q = (200)L + (100)K – (0.2)L2 – (0.1)K2     , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor of this function?

Company Z has the following data corresponding to the production function. Where (L) is the amount of the labor factor and (K) capital. Q=K0.4 L 0.6 a) Calculate the amount of production, applying the production function for each of the respective values of K and L. K L Q 10 80 30 160 50 320 70 640 90 1200 a) Graph the amount of production obtained on the Y axis, and with the labor input on the Х аxis b) Draw isoquant lines for each level of production, placing capital on the Y axis and labor on the X axis, to better appreciate the displacement.

Consider the production function q=√L+8K^(3).  Starting from the input combination (3,6), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?

Known function is the production of a commodityQ = 40X + 12X2 - 1.2X3a. Calculate how many units of input X in order to achieve maximum total productb. Calculate how many units of input X in order to achieve maximum marginal productc. Calculate how many units of input X in order to achieve maximum average product

The marginal product of labour is diminishing when: The marginal product of labour is larger than the average product of labour. The production function is convex. The production function is concave. The second derivative of the production function is negative.

A firm’s short-run production function is in the form of                        q = aLK +(bL^2)K −(cL^3)K , wherea, b, c > 0 are parameters. K is a constant. (a) Derive the marginal product of labor.(b) Find the level of L, expressed in terms of the parameters, at which the law ofdiminishing marginal product kicks in.

Identify the returns to scale in the functions below. Production Function a. q = 3L + 2K Returns to Scale constant increasing decreasing