Suppose that firm’s technology is given by the following production function: The prices of inputs are w = 2 and r = 2. a) Does this production function exhibit increasing, decreasing or constant returns to scale? Prove your answer. b) Derive the equation of firm’s long-run total cost curve (TC(y)), the long-run average cost curve (AC(y)), and the long-run marginal cost curve (MC(y)).

The long-rung production function of a competitive firm is f(L,K)= L1/3K 1/2 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. The price per unit of output is p. (A. What are the returns to scale of this production function?  (B. Find the long-run profit maximizing levels of capital, labor and output.

A production function for a good Q uses inputs of labor (L) and capital (K) and takes the form Q=LK. The wage is equal to $20 and the rental rate of capital is equal to $80. The firm has to produce a target qo. What is the equation for the firm's long-run total cost curve?

Consider the following long run cost function: TC = 8Q3 - 96Q² + 32Q Derive the expressions for marginal cost and average cost. What is the range of output over which production shows increasing returns to scale, and the range of output over which production shows decreasing returns to scale?

A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1,  x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?

A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1,  x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount?  please solve asap?

Consider a firm that produces a good using capital and labor. We denote by L the quantity of labor and by K the quantity of capital. In the short run, the firm has a fixed quantity of capital K. The short- run production function of the firm is given by f (K; L). The marginal product of labor (PmL) reaches its maximum when (a) the marginal product of labor is equal to the average product of labor, that is, PmL = PML. %3D (b) the total product q = f (K; L) %3D reaches its maximum. (c) Both of the above answers are correct. (d) None of the above answers are correct.

Suppose the production function for a competitive firm is y=f(x1,x2)= x1 1/4 x2 1/4 . The cost per unit of the first input is w1 and the cost of the second input is w2. A: What are the returns to scale of this production function? B: Find the cheapest input bundle, x1 and x2, that yields the given output level of y. C: Write down the formula of the firm’s total costs as a function of y. D: Are the average costs increasing, constant or decreasing in y? Are the marginal costs increasing, constant or decreasing in y?

Douglas Fur is a small manufacturer of fake-fur boots in Chicago. The following table shows the company’s total cost of production at various production quantities. Fill in the remaining cells of the following table.   On the following graph, plot Douglas Fur’s average total cost (ATC) curve using the green points (triangle symbol). Next, plot its average variable cost (AVC) curve using the purple points (diamond symbol). Finally, plot its marginal cost (MC) curve using the orange points (square symbol). (Hint: For ATC and AVC, plot the points on the integer; for example, the ATC of producing one pair of boots is $200, so you should start your ATC curve by placing a green point at (1, 200). For MC, plot the points between the integers: For example, the MC of increasing production from zero to one pair of boots is $80, so you should start your MC curve by placing an orange square at (0.5, 80).) Note: Plot your points in the order in which you would like them connected. Line segments…

A Chinese high technology manufacturing firm has a production function of 9=12L0.20K0.80 (based on Zhang, et al., 2012). It faces prices of w = $2 and r= $8. What are its short-run average variable and marginal cost curves? Let K be fixed in the short run. The firm's short-run average variable cost curve, AVC, as a function of K and q is AVC = $ (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) The firm's marginal cost curve, MC, as a function of K and q is MC = $. (Properly format your expression using the tools in the palette.)