Consider the following short-run production function (where L = variable input, Q = output):Q = 6L2 - 0.4L3a. Determine the marginal product function (MPL).b. Determine the average product function (APL).c. Find the value of L that maximizes Q.d. Find the value of L at which the marginal product function takes on its maximum value.e. Find the value of L at which the average product function takes on its maximum value.

Suppose that a firm has a production function given by: q= 10 L² K. The firm has 10 units of capital in the short run. Which of the following will describe the marginal product of labor (MPL) for this production function? Select one: a. Constant Marginal Returns to Labor b. Increasing Marginal Returns to Labor O c. Decreasing Marginal Returns to Labor

If the production function is f(x1,x2) = x1,x2.a. Show whether this production function exhibits increasing, decreasing or constant returns to scale.b. Show whether the average cost is increasing, decreasing or constant.

Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α

Consider a short run production function q = cL+K,using L units of labour and K units of capital: (c=0) 1.Compute the marginal product of labour.     2.Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.

Consider a short run production function   q=cL+k   where the value for c is 4, using L units of labour and K units of capital. Compute the marginal product of labour.   Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.

5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.

If a firm has the production function q = f(L, K) = L + 2K, then its technology exhibits:   constant returns to scale   increasing returns to scale   None of the above.   decreasing returns to scale   increasing marginal product

Consider a short run production function q = cL+K where the value for c=3, using L units of labour and K units of capital. a) Compute the marginal product of labour. b) Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.

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.