Find the elasticity of scale and the elasticity of substitution for the CES production function + x2rho 1/p, (x1; x2) = (x1" where 0 p< 1. rho
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- *Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.Define the followingE Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
- What is the elasticity of substitution of f(K, L) = KL²? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1 (e) 3/2 (f) 2 Which of the following represents increasing returns to scale? (a) f(K, L) = (K² + L²)¹/2 (b) f(K, L) = (K¹/2 + [¹/2)² (c) f(K, L) = (K + L) (d) f(K, L) = (K + L)² Suppose the production function for good q is given by q = (k¹/2+1¹/2)2. Consider the following three statements about this function: I. The function exhibits constant returns to scale. II. The function exhibits diminishing marginal productivities in both inputs. III. The function has a constant rate of technical substitution. Which of these statements is true? (a) All of them (b) None of them (c) I and II, but not III (d) II and III, but not IGive with diagram mandatoryUse the information in the graph to the right to find the values for the following at an output level of 35. 100 The marginal cost is S (Enter a numenc response using an integer.) MC ATC AVC 54 38 -- 17 35 Post
- AVC=10-0.03Q + 0.00005Q2TFC=60What is the TC function?What is the minimum AVC?To produce the next popular toy, a company has to pay a factory $250, 000 to set up the production line. They also have to pay $25 per item for the raw materials and labor. Write function for the average cost to produce x items. Then describe what happens to the average cost as the factory produces a large number of toys.suppose the Total Revenue function for a product is given by R(x)=V0•1x+0-2x² (R-4,x--u) a) Find the Rate of change in Tota) Revenue or Morginal Revenue . a) b) Find Margina) Revenue nhen x=4 units are sold and slate nhatitpredicts for the sale of the next unit c) Firid the Actual change in To tol Revenue uhen productm Level is ingeased from 4 to 5 units di Esplainany discreponcy hetncen parls (1) and (c)resuHs mathemohie ally / Graphically d)
- Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 1 f(x₁, x₂) = (x³ + x2)³. Solution: We first calculate the marginal products: 2 fx₁ = 3 + = x1fx1 -+ 2 2 10 - ² ( x² + x ) ( + x^²) = ( + + + + ² ) 15 ²0 x² -2/3 x₂ + x2fxz Elasticity of scale = _1₁_+_*__*(+)´<°¸«d«)*;»_ f(x1, f(x1, ‹2)² = -2/3 r2/3 = TRS = t (where TRS = =t). ⇒ r = t³/² ⇒ ln(r) = ln (t) and o = -2/3 dln (r) dln (t) To get elasticity of substitution, we first need TRS and denote r = 1 x3 X1 TMS - F (+4+2)0 = fx₁ fx₂ 2 1 + x²) x₂² MIN x2 3 -2/3 (x² -2/3 2 2/3 2/3 x1 -2/3 = r²/3 x¹/3 + 1/3 = 1.Fig 2.1 illustrates the law of diminishing returns in seeking the optimum system (or component) performance and hence the need to balance the performance against the cost. Give examples of two pairs of characteristics other than performance versus cost where optimizing one frequently competes with the other, and briefly explain why they do.Solve the following problems related to optimization problemsA restaurant finds that, when priced at $8, it sells 60 sandwiches a month. For every dollar that the restaurant discounts their sandwiches, they sell 5 more per month. If the cost to the restaurant to make a sandwich is $4, find the price that the restaurant should charge for a sandwich to maximize its profit. must show all steps
