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- Differentiate between the Iso quant and Iso cost. If Iso quant is represented by Y = L0.5K0.5. and wage rate w = 10, rent of capital r = 5 and total budget M = 300, then find out the optimum combination of inputs and the output produced by these inputs.Consider the market for labor where both firms and workers are price takers. Output is produced using capital and labor.The marginal product of labor can be described by: 200 – 4L, where L is the number of workers hired. The price of the good produced is 5 per unit. a. Illustrate the demand for labor. Be sure to note the specific value of the vertical intercept. b. Suppose that the competitive firm must pay 100 for each worker. Determine the number of workers hired. (Determine the total income to capital. Show your work for both parts. c. Suppose that the price of the good rises but that the wage remains the same. Illustrate how the optimal choice of labor would change. No need to do the explicit calculation; just show the outcome and briefly explain.a) Find Bob the builder’s total cost function. Use the cost minimization conditions to find Bob the builder’s conditional demand for labor L^(q) and equipment K^(q). b) Substitute the conditional demand for labor and equipment and the current wage rate and rental cost of equipment in the expression TC = wL^(q) + rK^(q). c) Suppose Bob charges $4,000 for each veranda, how many verandas does he build? How many workers does he hire? How many pieces of equipment does he rent?
- Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72V3 given froduction function F=K^1/4 L^1/16 price of capital and labor are v and w 1)find short run cost function with quantity X, and that there are Y amount of capital purchased 2)find the long run contigent demand for capital and laborFree competition company produces a good Y with the following product functions Y=1/2*L1/2, where L is labor a) How large is the company profit, calculate and illustrate it graphically. b) The salary is doubled to 20kr, how will this affect the company's demand and adjustment in the market? Show graphic and mathematically.
- Course: Introduction to Economics - Labor Market This exercise is presented again. There are still no answers. Please, I need a real expert. Thank you You've been asked to solve an analytical example to illustrate concretely effects of minimum wage and labor income tax legislation on employment and, therefore, unemployment. For this, you have decided to study Labor Demand of a firm whose production function is given by: Y = A K1/3 L2/3For simplicity, you decide to assume that A = P = K = 1 , where A is factor productivity, P is price of the good sold by firm and K is amount of capital hired by firm. Recall, moreover, that optimal decision of any economic agent can be reduced to an equality between marginal revenue and marginal costs. In particular, firm will hire workers up to a point where marginal revenue (MR) of their labor equals marginal cost (MC). Given production function you have decided to use for analysis, marginal productivity (MPL) of labor is given by: MPL =…A purely competitive firm has a single variable input < (labor), with the wage rate. W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) what is the first-order condition for profit maximization ? Give this condition an economic interpretation. (c) What economic circumstances would ensure taht profit is maximized rather tahtn minimized?Consider a firm that is perfectly competitive in the market for inputs and outputs. Thefirm hires two types of workers: low-skill (high school graduates and high school dropouts) andhigh-skill (undergraduate and postgraduate degree) workers. The firm compensates high-skilledworkers at the rate wH and low-skill workers at the rate wL. It produces the output subject to aCobb-Douglas production technologyF(L,H) = (AH)α(L)β,where H - is the amount of high-skill hours, L - the amount of low-skill hours, and A - thetechnology parameter that augments the productivity of the high-skill labour. 4. In the short run, the firm cannot increase the amount of high-skill labour . Derive the1short-run demand for low-skill labour.5. What is the substitution effect of the wage increase in the short-run?6. Derive the long-run cost-minimizing demands for high- and low-skilled labour. Show thesolution to the cost-minimization problem on the graph
- Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s costminimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…