Consider the following cost function:C(W1;w2: y) = w1 1/2w2/2,2.(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 answers.You may either enter your answer in the answer text box or upload a document displaying your work.For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).BI U S ParagraphA vArial10pt...O WORDS POWERED BY TINY>!!!

The following cost function is given: C(w1;w2;y) = w11/2 w21/2 y2 w1 is the price of Input 1 w2 is…

Answered: Consider the following cost function:…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.7P

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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)
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 and K 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. At what 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 input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)
Given the input-output matrix below, find the output matrix if final demand changes to 500 for water, 180 for electric power, and 800 for agriculture. Industry Electric Power Industry: Water Electric Power Agriculture Other Water 200 100 300 400 The output matrix is X= (Round to two decimal places as needed.) 480 120 240 360 Agriculture Final Demand 180 240 120 60 290 140 600
Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?
Q.No.3. Consider the production function: (3) Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of X, the output will be maximum? (b) If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?
(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. Let input prices be (wK, WL) and output price be p. The production function is given by f (K, L) = min [√K, L]. (b) Derive the cost function. Use the cost function to derive the output supply function.
The cost function for producing x items is C(x)=x2-3x+625. a.Find the average cost function. b.What is the minimum average cost? c.Find the marginal cost function. d.Is the point of intersection of the average cost and marginal cost function the same which produced the minimum the average cost? 2.Determine where the function f(x)=4x3-3x2+6 is concave and where it is convex. 3.An efficiency study conducted for Spektra Electronics Showed that the number of Base Commander handsets assembled by the average worker t hours after starting work at 8 a.m is given by N(t)=-t2+6t2+15t (0t4) At what time during the morning shift is the average worker performing at peak efficiency?
To produce a recorded DVD, a firm uses one blank disk D and the services of a recording machine M for one hour. The production function in this case is given by: Q = min{D, M}(a) Using this production function, find the firm’s demand function for recording machine-hours M.(b) ) Draw the total product, average product, and marginal product of M curves for the production function identified(c) Let PM denote the hourly price of renting the recording machine M and PD denote the price of one blank disk. Use your answer from (b) to calculate the firm’s short-run total, average, and marginal cost functions.
Find the marginal values for functions a, b, and c given below and evaluate each at Q=100. a) C(Q) = 540 + 6Q where C(Q) is the total cost function and Q is the level of production. b) R(Q) = 9Q where R(Q) is the total revenue when Q units are transacted at a constant price of P=$9. c) R(Q) = P(Q)Q, where P(Q) = 40 – 0.1Q, is a demand (inverse) function showing the dependence of price on quantity demanded Q.
1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁
A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L where K and L are levels of capital and labor in production respectively. (a) Find the optimal bundle of capital and labor to produce 400000 units of output, if the wage is w=$8 and the rental price of capital is r=$1. Also, find cost of producing 400000 units of output. (b) Suppose that in the short run this firm must use 40000 units of capital but can vary its amount of labor freely. How does optimal number of labor and cost of production changes? (consider prices and quantity given part a) (c) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (d) If the wage is w=$10 and the price of output is p=$2, how much labor will the firm demand in the short run? (e) Write down an equation for the firms short-run demand for labor as a function of w and p. (f) Write down an equation for the firms short-run cost function as a function…

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