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.
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Q: A firm’s production function is Q = 600*L -1.0*L2. The firm is currently employing 83 units of…
A: A firm’s production function is Q = 600*L -1.0*L2
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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 Otherwise
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- Find the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!Question 2: For this problem you will analyze the elasticity of substitution and the isoquant graphs for two different production functions F₁(K, L) = 4K + 2L F₂(K, L) = K²/³ [1/3 (a) Graph the isoquant for F₁(K, L) = 4K+2L that represents an output of 8. Be sure to show your work and label the axes clearly (b) What is the marginal rate of technical substitution (MRTS) for F₁ ? (c) What is the elasticity of substitution for F₁ ? /1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…
- What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2*Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.You are an accountant for a manufacturer of radios. The demand function for the tablets is p= 40– 4x² where x is the number of tablets produced in millions. It costs the company $15 to make a tablet. (i). Write an equation for the manufacturer's profit as a function of the number of tablets produced. (ii). The company currently produces 1 million tablets and makes a profit of $21,000,000, but you would like to scale up production a bit. What greater number of tablets could the company produce to yield the same profit?
- If a firm has the production function f(k, I) = (2k1/4 + 14)" what is the firm's elasticity of substitution? O a. G = O b. o = O c. o = 1 O d. a = 2 O e. o = 4 114 -/2Exercise A.5 A company operates with production function q-K¹/2 [1/2 a) What type of returns to scale does this production function present? As production varies, how would you expect long-term average costs to evolve? b) Assume that the firm's capital equipment is fixed and equal to K = 100 units. Find the firm's short-run production function and the marginal productivity of labour and graph these functions. As production varies, how would you expect marginal costs to evolve in the short term? c) If the prices of capital and labour are r = 8€ and w = 2€ respectively, obtain the expression of the short-run total cost function of the firm. b) Obtain the expressions of the functions of short-term average total costs, average variable costs and marginal costs of this company. Find the production level for which the average total cost is minimized and the corresponding average total cost level. d) Indicate the value of the average total cost, the average variable cost and the marginal cost…Suppose that a firm can not give up one input in an exchange for the other and still maintain the same level of output. Calculate the elasticity of substitution in this case and elaborate on your answer.
- Consider the production function Q = 2(KL)0.5 c) What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?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.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?
