Profit Maximization. Assume that the output price p, wage rate w, and rate of return to capital y are exogenous. Suppose further that output is produced using inputs of labor / and capital k. Technology is represented by q = f(l,k); where fi fx>0; fu> fx <0; ₁x = fx >0; and SS-S >0 ak at al Find- aw' ar' ap

Profit Maximization. Assume that the output price p, wage rate w, and rate of return to capital y are exogenous. Suppose further that output is produced using inputs of labor / and capital k. Technology is represented by q = f(l,k); where fi fx>0; fu> fx <0; ₁x = fx >0; and SS-S >0 ak at al Find- aw' ar' ap

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section7.A: Appendix: A Closer Look At Production And Cost

Problem 1AQ

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Please don't copy ans Economics You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 . a. What are costs as a function of output for each individual factory? b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory? c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions? d. It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay…
22.5 Recall that Touchie McFeelie's production function for comic books is .1J1/213/4. Suppose that Touchie can vary both jokes and cartoonists' labor. If old jokes cost $2 each and cartoonists' labor costs $18 per hour, then the cheapest way to produce comics books requires using jokes and labor in the ratio J/L= (a) 9. (b) 12. (c) 3. (d) 2/3. (e) X+ PC X4.0 Show Transcribed Text 000 please explain this question and the correct answer is 6. Thanks.
Coosider the production function characterizing garri plant as: Q= 20L + 60k - L^2 - K^2 If total outlay for both capital, K =N50, and a Labour, L= N20, is N4,600. Find: a. The optimal quantity of K* and L* to be employed. b. Calculate the maximum possible output of garri that the plant can produce.
4. Profit Maximization. Assume that the output price p, wage rate w, and rate of return to capital rare exogenous. Suppose further that output q is produced using inputs of labor I and capital k. Technology is represented by q = f(1,k); where fi, fx > 0. fu fkk 0. ; and ək Əl Find aw'ar fufkk-fi >0
10. An isoprofit curve will have which of the following properties? (a) If an extra unit of capital is used, output will rise by AQ = MP₁AL (b) If an extra unit of capital is used, the value of the extra output produced would be PMPKAK (c) If profits are being maximised, then profits can only be increased by using a different combination of inputs (d) If an extra unit of capital is used, the cost of producing the extra output produced will be rAKMPK (e) Profit maximisation will occur where the marginal rate of substitution is greater than the ratio of prices.
2. A firm uses capital (K) and labour (L) to produce luxury office chairs. The production technology is given by Q = K³/4L¹/4, where Q is the number of chairs produced. (a) What is the marginal product of capital and the marginal product of labour for this firm? (b) Does this production function display decreasing returns to scale, constant returns to scale or increasing returns to scale? Justify your answer. (c) Suppose that the firm has a contract with a national retailer who purchases Q office chairs from them per day. The firm faces prices PK = r and PL = w for capital and labour respectively. Find the firm's conditional input demands. (d) Now suppose that the firm's contract with the upstream retailer is coming to an end and they are considering whether to extend it or not. The retailer will purchase 1000 chairs per day at £50 per chair. If the firm does not extend their contract then they can sell their chairs locally and will face an inverse demand curve P(Q) = 500 - Q. Assume…
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What is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?
4) Please indicate whether the following production function has the characteristic of CRS, IRS and DRS. (a) F(Z1, Z2)=(Zı+Z2)/2 1. CRS 2. IRS 3. DRS 4. None of the above (b) F(K, L)=[aKP +(1-a)Lº ]Ve, (1>a>0, 1>p) 1. CRS 2. IRS 3. DRS 4. None of the above
Describe where the law of diminishing marginal productivity begins for We R' Write. We R' Write currently uses 75 workers on the production line per day. Given the calculations in the table, is this number optimal? Why, or why not? If you could make a suggestion regarding the optimal number of workers We R' Write should use on the production line, what would it be? Why? Number of Workers per Day Pens Produced per Day Average Product Marginal Product Price per Pen Total Value Product Average Value Product Marginal Value Product Price of Worker per Day 0 0 --- --- $3.50 $0.00 --- --- $560 15 1,000 66.67 67 $3.50 $52.50 $233.33 $233.33 $560 30 2,700 90.00 113 $3.50 $105.00 $315.00 $396.67 $560 45 5,100 113.33 160 $3.50 $157.50 $396.67 $560.00 $560 60 7,900 131.67 187 $3.50 $210.00 $460.83 $653.33 $560 75 12,000 160.00 273 $3.50 $262.50 $560.00…
13. Suppose you have a production technology given by f(x1, x2) = min{2x₁, x2} and you are producing at the point where x₁ = 10 and x₂ = 20. (a) Explain in words what we mean (generally) by the ‘marginal product' of an input in production. (b) For the production technology in this question and the initial point x₁ = 10 and x2 = 20, what is the marginal product of a small increase in input 1? (c) Suppose input 2 increases and you are now at the initial point x₁ = 10 and x2 = 30. Relative to your answer in part (b), does the marginal product of input 1 decrease, increase, or stay constant? Explain briefly.