b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L andK can vary with production. Compute the input demand functions as a function of Q. (4 Points)c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. Atwhat prices of textile will the producer shut down production. (3 Points)d Now suppose Q=10LK. The market prices of inputs are as in subpart (b) above. Compute the inputdemand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn.(5 Points)

b) Suppose the production function is Q = 2L + 3K, where Q represents the output quantity, L is the…

Answered: b Now suppose Q = 2L +3K. Let the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
(a) For the cost function C(w1, w2, y) = 2y²w} w, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (xf(w1, w2, y), a(w1, w2, y)). (b) Consider the production function f(r, y, z) = Vry + rz+ yz. Find the scale elasticity SE at (x, y, z) = (1,2, 3), (5, 1,6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer. (d) Suppose that there are the infinite number of potential firms that produce the identical output good y under the cost function C(y) = + 3. Assume free entry and exit. Find the long-run equilibrium output price p, the amount of the output that each firm in the market produces in the long-run equilibrium, and the value of profit that each firm earns in the equilibrium.
1 1 Consider the following cost function: c(w₁, W₂, y) = (w₁ + w₂)¹ y² (a) Find the marginal cost function, the average cost function, the supply function, and the demand function for input 1. (b) Sketch the supply curve and the demand curve for input 1. (c) What is the effect of an increase in the price of input 2 on the supply curve and the demand curve for input 1? Illustrate your answer. Solution: (excluding graphs) 1 1 дс MC = = 2 (w² + w²₁) ³y ду 1 _c_ (w² +w² )*y² _ y AC = -=-=-=- y 1 Supply: p =MC ⇒p = 2(w₁ +w₂₁) ¹y 1 1 1 = (w₁² + w²) ³ y To get demand for input 1, we use Shephard's lemma: x₁ = Cw₁ (w, y) = 4 (w^² + w² ) ² (; w₁, ²³y²) = (w ² + w² ) ² (w,₁ ²,²)
is profit maximisation seen as local minimum or maximum? Is part (b) the correct way of doing first derivative? There is image of the questions, another image of the answers of part (a) and (b).
Please select all that are true regarding Minimum Efficient Scale (MES): if the quantity demanded is equal to Qmes, then the lowest cost solution is for one firm to supply the market MES is the quantity produced where average costs for a firm are at a minimum Long run average costs include fixed cost steps as quantities (scale) increase Quantities (x-axis) less than MES exhibit decreasing returns to scale due to diminishing marginal returns Short run average cost curves are for a given level of fixed cost, individually MES is the quantity demanded where total costs for a firm are at a minimum Quantities (x-axis) greater than MES exhibit decreasing returns to scale due to diminishing marginal returns Average costs do not include fixed cost since they don't change
A5
1/3 1/3 Assume y = f(x1, x2) = x1 x2 . If the input prices are w₁ and w₂ what is profit maximizing y level of output? What is the profit?
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.
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
1. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.
Please show step by step
Problem 5 Suppose that a firm has a production function f(K, L) = 12L¹/3 K¹/3 and that w and r are input prices and p is output price. The firm does not change those prices. a) Show that the firm's profit π is a concave function of (K, L). b) Find (K*, L*) that maximizes the profit, as a function of (w,r, p).

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