3.Assume that a firm which produces an output according to the following function isattempting to cost minimize in the long run.q=f(K, L) = (.5K¹/2 + .5L¹/2)¹/2a. Without solving the problem mathematically, set up the equation for scale elasticityand explain how you would use it to check whether this production function exhibitsincreasing, decreasing, or constant returns to scale.b.Compute this firm's cost minimizing (quantity constant) input demand functions.C.What are the firm's total cost and supply functions.d.Assuming K is fixed at 36, what is the firm's short run cost function?Assuming the firm is operating in a competitive market with a market price of P,e.In the profit maximizing optimization, what do the first order conditions and secondorder conditions ensure?f.Compute this firm's profit maximizing demand functions for K and L.g.What three functions can be derived using the profit function? And how?

Given production function q=f(K,L)=(0.5K12+0.5L12)12 Price of labor=WPrice of capital=r

3. Assume that a firm which produces an output according to the following function is attempting to cost minimize in the long run. q= f(K, L) = (.5K¹/2 + .5L¹/2)1/2 a. Without solving the problem mathematically, set up the equation for scale elasticity and explain how you would use it to check whether this production function exhibits increasing, decreasing, or constant returns to scale. b. Compute this firm's cost minimizing (quantity constant) input demand functions. What are the firm's total cost and supply functions

3. Assume that a firm which produces an output according to the following function is attempting to cost minimize in the long run. q= f(K, L) = (.5K¹/2 + .5L¹/2)1/2 a. Without solving the problem mathematically, set up the equation for scale elasticity and explain how you would use it to check whether this production function exhibits increasing, decreasing, or constant returns to scale. b. Compute this firm's cost minimizing (quantity constant) input demand functions. What are the firm's total cost and supply functions

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. A competitive firm uses two variable factors to produce its output, with a production function q min{x₁, x₂}. The price of factor 1 is $8 and the price of factor 2 is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x₁. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no butput. What is the smallest integer price that would make a firm willing to produce a positive amount? b. d. $44 $41 $29 $13 $21
1. If the Örmís production function isF(K;L) =K(L+ 2), derive the short-run total cost functionSTC(q;r;w;K). 2. The total cost of producing infant formula isCF= 30+qF. The total cost producing disposable diapers isCD= 30 + 0:5qD. The total cost of jointly producing them isCJ=70 +qF+ 0:25qD. Does this production process exhibit economies of scope?
Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…
Could you solve d,e,f ? Thank you
ONLY answer question b. relative to question a.
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.
3
K Suppose that a firm's production function is q=5x in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is $625 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). The total cost of producing ya level of output q is A. C(q)= 1,000. OB. OC. OD. OE C(q)= 1,000+ C(q)= 1,000+ C(q) = 1,000+ 625q² C(q)= 25 q² 25 625q² 25 0.5 q B Dollars per unit of output 2000- 1800- 1600- 1400- 1200- 1000- 800- 600 400- 200- a 12 14 10 Quantity nchack 18 (1) Incorrect
3. Suppose a firm has the following production function q = LK4. Let the unit price of capital be 1 and the unit price of labour be w. a) Use the Lagrangian method to find the optimal number of each input used to produce an order of q'units b) Find the long-run cost function. c) How does the cost function change if the wage rate changes?
3
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
handwrite it out step by step