Consider a production function: Q = f (L), where Q represents the output and L is the factor of production. Let w be the per unit price of factor L and p be the per unit price of output Q. Using the Envelope theorem determine the supply function and the factor demand function.
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Consider a production function: Q = f (L), where Q represents the output and L is the
factor of production. Let w be the per unit price of factor L and p be the per unit price of
output Q. Using the Envelope theorem determine the supply function and the factor
demand function.
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- Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. Find the profit function π(K,L) and simplify Find the first order conditions to maximize the profitSuppose that the production of a certain product only requires one input, labor, and that the additional production diminishes by half after the last input. On the other hand, the demand of the good can be described using the equation Q = 10000 – P/10. The total product of the second unit of labor is 3,000 unite. Finally, each additional worker requires P1,000,000. Given the following information, answer the following questions: What is the marginal revenue product of the third unit of labor? Answer: 500 How would you characterize the marginal revenue product of labor? How would you characterize the labor market that this firm faces?Production Function and Input Demand Consider the production function Q = K + √L. Derive the inputdemand curves for L and K, as a function of the output Q, inputprices w (price of labor services) and r (price of capitalservices). Does the production function exhibit IRS, CRS orDRS?
- Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. a) Find the profit function π(K,L) and simplify b) Find the first order conditions to maximize the profit c) Find the value function for L and K, i.e the functions L* = L*(p,r,w) and K* = K*(p,r,w) and simplify. What is the meaning of the value functions d) Find the best production quantity and the maximum profit, i.e Q*(P,r,w) and π*(P,r,w) simplify resultsLet the production function of a firm is given as q=(x0.5 +y0.5)2 Where x and y are inputs and wx is the price of input x and wy is the price of input y. a) Assume the firm has a limited budget to spend on buying input. Find the cost-conditional input demand function for each input. b) Now, assume the firm has no budget restriction but it has a production quota. Find the output-conditional input demand function for each input. c) Find the cost function of the firm. d) Assume the firm has no budgetary or production restrictions and set up the profit maximization problem. e) Write the conditions that need to be met to find a non-zero output that maximizes profits.A firm produces its product using only labor. Its production function is Q= 20L -L, where Qis the number of units of output produced and Lis the number of labor hours used. The firm purchases labor in a competitive labor market at the going wage rate of w = $12 per hour. The firm sells its output in a competitive market at the market price of P= $5. To maximize profit, the firm should use hours of labor and produce units of output. (Enter your responses rounded to two decimal places.)
- Suppose that the production function is given by y = 2x0.5 The price of x is $3 and the price of y is $4. Derive the corresponding VMP and AVP functions. What is MFC? Solve for the profit-maximizing level for input use x.Consider the following production function: y = lnx1 + lnx2, where x1>0, x2>0. Is it homogenous? Is the input requirement set monotonic and convex? Find its elasticity of substitution.Suppose that a firm's production function is given by: 150- Q = 14L -12 140- 130- 120- 110- 100- for L=0 to 7, where L is labor input per day and Q is output per day. Derive and draw the firm's demand for labor if the firm's output sells for $10 in a competitive market. The marginal product of labor (MP, ) is 14 - 2L. Using the line drawing tool, draw the firm's labor demand curve. Label this curve D, . 70 Carefully follow the instructions above, and only draw the required objects. 50- 30- 20- 10- 10 Quantity of labor (hours) Price of labor
- Exercise: A firm produces output according to the following production function: q = A K1/4 L1/4 The price of capital is labeled r and the price of labor is labeled w and there is a set-up cost labeled F. Solve the cost minimization problem and do the following: If A = 6, r = 4, w =25 and the firm wants to produce q = 36, Determine this firm’s demand for capital K*. Group of answer choices a)15 b)45 c)90 d)60Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?Given a demand function of P = 114 - 7Qd and supply of P = 27 + 6Qs, the utility function U = Qx0.4Qy(1-0.4) and the consumer budget 160 = 8Qx + 7Qy along with the firm production function Q=K0.4₁0.7 with the isocost 289 = 23K +14L. The economic growth factor is 2.2. What is the marginal rate of substitution between good X and good Y at Qx= 4 and Qy=18 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).