Show that the two-input CES production(attached) has DRS, CRS, or IRS depending on whether B (beta) is smaller than, equal, or greater than 1.
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Show that the two-input CES production(attached) has DRS, CRS, or IRS depending on whether B (beta) is smaller than, equal, or greater than 1.
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- 1a) Consider the production function Q = 0 + 6L + 5L2 - .2L3. The range of labor covering Stage II of production is ____ to ____. You can use Excel spreadsheet or otherwise to answer this question. b) A firm’s production function is Q = 600*L -1.0*L2. The firm is currently employing 83 units of labor. What is the elasticity of production? You can use a excel spreadsheet or otherwise to answer this question c) A firm’s LRTC = 600Q - .5Q2 + .001Q3. At what level of output does the firm experience minimum efficient scale? Use either Excel Spreadsheet, Excel Solver or OtherwiseCalculate the Lagrange multiplier of the cost minimization problem with a CobbDouglas production function, and show that it is equal to the derivative of the cost function with respect to output (the marginal cost).Take a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.
- Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplierLet 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?
- For the production function q = f(K, L) the ratio of the percentage change on K/L with percentage change on PK/PL is called elasticity of substitution. Write down a constant returns to scale Cobb-Douglas production function and find its elasticity of substitution for the K = 10, L = 7, PK = 4 and PL = 3 levels.Q.No.3. (a) What is the input use level for total value product maximization for the following function? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23 Q.No.3. (b) Briefly make a comparison between output maximization criteria and profit maximization criteria with respect to necessary and sufficient conditions?Let 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.
- Consider the supply function: Qs = 60 + 5P – 12 PI + 10F , Where Qs = quantity supplied, P = price of the commodity, PI = price of a key input in the production process, and F = number of firms producing the commodity. (a)Derive the equation for the supply function when PI =$90 and F = 20. (b) Using the supply function from part (a), calculate the quantity supplied when the price of the commodity is $300 and $500. (c)Derive the inverse of the supply function in part (a). using the inverse supply function; calculate the supply price for 680 units of the commodity. Give an interpretation of the supply price.Find the supply function and the input demand functions for the CES production function: f(x1,x2)=A(αxρ1 +(1−α)xρ2)β/ρ, where A > 0, β > 0, 0 < α < 1, and 0 ̸= ρ < 1.Given the following cost function, determine the underlying production function. 1 2C(m, w, y) = 10mwy, where y is the output and m and w, are the prices of two inputs x1 and x2 respectively.