From the production data in the table below, calculate the VMP for the 2nd unit of labor. Assume the wage rate is $80 and the price of the firm's output is $5. (Give the numeric value only for your response; do not include commas, dollar signs, etc.) Capital Labor Output (Q) 100 100 1 20 100 2 44 100 3 66 100 4 84 100 96 100 104 100 7 98

Consider a firm with Total Output function (Production Function) given by Q = 6L2 – 0.4L3, where L is variable labor input. The firm is faced with the decision to hire the optimal number of workers in order to maximize its output level.   (a) Obtain the Marginal Product function.   (b) Find the Average Product function.   (c) Determine the level of employment that would maximize the firm’s output level.   (d) Verify that the second-order condition is met for the firm's output maximum.

A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is: X=-0.2L3 + 18L2 + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A t what weekly output is marginal cost equal to average variable cost? if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?

From your knowledge of the relationships among the various production functions, complete the following table: Variable Input L Total Product Q Average Product AP₁ Marginal Product MPL 0 0 1 2 3 4 5 6 7 30 二二二二 120 20.00 24.00 15 || 45 -15

A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?   $20 $10 $50 $100

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?

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

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL= $1 and PK = $1.What is the smallest total cost necessary to produce Q = 100?

Assume that total fixed costs are $46, that the average product of labor is 5 units when 10 units of output are produced, and that the wage rate is $12. If labor is the only variable input, what is the average total cost of producing 10 units of output?