Let L represent the number of workers hired by a firm and let Q represent that firm’s quantity of output. Assume two points on the firm’s production function are (L = 12, Q = 122) and (L = 13, Q = 130). Then the marginal product of the 13th worker is

Carefully reproduce and fill in the blanks in the table below:Where VMPL is the Value of the Marginal Product. 6 Marks(b). If a production function is given by the equation: Q = 12X + 10X2 - X3, whereLabour Wage Rate Price Output MPL VMPL Marginal Profit0 400 3 01 400 3 762 400 3 2483 400 3 7924 400 3 7845 400 3 11006 400 3 14167 400 3 17088 400 3 19529 400 3 212410 400 3 22

Question 5 (HPW11.5, Problem 80, p. 527)A monopolist who employs m workers finds that they produce:𝑞 = 2𝑚(2𝑚 + 1) *&Units of product per day. The total revenue, r (in dollars), is given by:𝑟 = 50𝑞:1000 + 3𝑞a) What is the price per unit (to the nearest cent) when there are 12 workers?b) Determine the marginal revenue when there are 12 workersc) Determine the marginal-revenue product when m =12.Note: round your answers to 2 decimal places

A manufacturer determines that m employees will produce a total of q units each week. The relation between the number of employees and the quantity is given as: 𝑞 = 5𝑚2 + 2𝑚 + 4. Given that the demand function for the product is given as 𝑝 = 1000 𝑞+8 , determine a. The rate of change of price with respect to quantity b. The rate of change of price with respect to the number of employees c. Determine the marginal revenue when the number of employees is 15

Your enterprising uncle opens a sandwich shop that employs seven people.The employees are paid $32 per hour and a sandwich sells for $8. If the market for sandwiches is competitive, and your uncle is maximising his profit: a) What is the value of the marginal product of the last worker he hired? b) What is that worker's marginal product? c) Suppose that your uncle purchases a new machine that increases the marginal product of each worker. How will this affect the number of workers that he hires? Explain.

Consider a firm with production function given by 𝑄(𝐾, 𝐸) = 𝐾^1/3𝐸^2/3 K denotes units of capital and E denotes units of labour. Capital is fixed at 27 units. The firm’s output decision has no effect on the price of output or the wage (w). (a) The firm is profit maximizing and can sell output for $12 per unit. Solve for the firm’s labour demand function. That is, express E as a function of w. Note that for this production function, the marginal product of labour (MPL= MP_e) is MP_E = 𝜕Q(𝐾, 𝐸)/𝜕E = 2/3 𝐾^1/3𝐸^−1/3 Show your formulations and derivation.