If a firm has a production function of the form: Q = LK³, what can we conclude? The firm has convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. The firm has a linear production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. O The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital.

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.

Question # 1: Majeda wrote the following answer on her microeconomics examination: “Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So, when all inputs are doubled, output must be less than double." How would you grade Majeda's answer? Question # 2: Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed-portions production function, what would the firm's expansion path be? Question # 3: Suppose that a firm's production function is q = 30√L. In the short run, where there are fixed costs of $2,200, and labor is the variable input whose cost is $6,300 per units. What is the total cost of producing 20 units of output?

Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes

Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False

Consider the production function: Y = z.f(K,N,L) where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land.

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The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…