QUESTION 4Consider the following cost function:C(w1;w2; y) = (w1 1/3 + w21/3,3,2(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 answersYou 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 ParagraphE AArial10pt!!!

Cost function: C(w1;w2;y) = (w11/3 + w21/3)3 y2 w1 is the price of input 1 w2 is the price of input…

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)
The data below shows tabulation on the production of a hypothetical product.Output (Q) Total cost (TC)Units Kshs.0 - 251 - 322 - 383 - 424 - 485 - 586 - 677 - 788 - 98i. Using the above data, determine:· Total fixed cost · Average variable cost schedule · Marginal cost schedule Suppose this product is produced on a perfect market and the price of the commodity = 10, determine the output Q that will maximize the profits. What is the maximum profits achieved by the firm?
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?
12. If the demand function for a product is p = 100 – 2x where is price in dollars and x is the number of units sold, and the average cost function for a product is C(x) = 100 +4 where x is the number of units sold and C is dollars per unit, what is the maximum profit? Answer and Work Explanation of Work
The table above shows the total cost function for a typical firm producing hats in a perfectly competitive market. The market price for hats is $9 per hat. (a) Calculate the average variable cost of the fifth unit. Show your work. (b) What is the firm’s profit-maximizing quantity of hats? Explain using marginal analysis. (c) If the rent of the building the firm occupies increases, what will happen to the firm’s profit-maximizing quantity of hats in the short run? Explain. (d) Draw a correctly labeled graph showing the firm’s demand and marginal cost curves, and show the profit-maximizing quantity of hats, labeled Q*.
(a) Find the conditional input demand function for inputs 1 and 2, as well as the cost function for this firm. (b) What is the firm's marginal cost when it is producing y units of output?
Question one Assume that the firm's operation is subject to the following production function and price data: Q=3X+5Y-XY Px = $3; Py = $6 Where X and Y are two variable input factors employed in the production of Q. (a) In the unconstrained case, what levels of X and Y will maximize Q? (b) It is possible to express the cost function associated with the use of X and Y in the production of Q as TC = 3X+6Y. Assume that the firm has an operating budget of $250. Use the Lagrange multiplier technique to determine the optimal levels of X and Y. What is the firm's total output at these levels of input usage? (c) What will happen to the firm's output from a marginal increase in the operating budget?
Q3) the demand function and total cost function for a product are 6P = 660 − 3Q, TC = 80 − 20Q2 + 600Q (a) Write down expressions for: (i) Average cost, (ii) marginal cost, (iii) total revenue, (iv) Marginal revenue, (v) Profit. (b) Determine the values of Q for which total cost is a maximum. Calculate the maximum costs. Calculate the profit when total costs are a maximum. (c) Determine the value of Q for which profit is a minimum. What is the minimum profit?
Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?
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…
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 ? /

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