Suppose that there are two goods X and Y produced in perfectly competitive industries facing constant returns to scale in production. There are two inputs labour and capital, denoted by L and K respectively. Denote prices of goods X and Y by Pxand Py respectively; price of L by w and of K by r. a) What type of relationship do you expect between relative prices of inputs used to produce these goods and those of the goods? Explain why. b) Explain the meaning of factor intensity. When will you consider good X to be labour intensive relative to good Y? What changes in these intensities would you expect if relative price of labour increases? c) If X is labour intensive and Y is capital intensive in one nation, does it also have to be the case in the other nation? Why or why not?

Suppose that there are two goods X and Y produced in perfectly competitive industries facing constant returns to scale in production. There are two inputs labour and capital, denoted by L and K respectively. Denote prices of goods X and Y by Pxand Py respectively; price of L by w and of K by r. a) What type of relationship do you expect between relative prices of inputs used to produce these goods and those of the goods? Explain why. b) Explain the meaning of factor intensity. When will you consider good X to be labour intensive relative to good Y? What changes in these intensities would you expect if relative price of labour increases? c) If X is labour intensive and Y is capital intensive in one nation, does it also have to be the case in the other nation? Why or why not?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.12P

See similar textbooks

Similar questions

(A) Suppose the production function for T-shirts can be represented as q = L0.5 KO.5. Show that the marginal productivity of labor diminishes in the short run. What is the cost minimizing bundles of labor and capital in the long run for T-shirts where w = and r = 10 when q=100 units?
Suppose the production function for high quality brandy is given by : Q = √KL Where q is the output of brandy per week and L is labor hours per week ., in the short run K is fixed at 100, so the short run production function is Q = 10√L a. Ifthecapitalrentsfor10$andthewageare5$perhour.,writetheshortruntotalcost function. b. How much will the firm produce at a price of 20$ per bottles of brandy ? c. Howmanylaborhourswillbehiredperweek?
A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?
Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Herproduction function is given by: Q(T,D) = (T1/2 D1/2)1/2*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worryabout restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns toscale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputsrequired to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
New taskFor a producer under complete competition, the following production function applies. Q = F (K, L) = KL where Q is the size of production, K is the size of the capital investment and L is the amount of labor. Assume that the price of capital, r, is 5 and that the salary, w, is 10. a) Assume initially that the capital is locked at 4 units. How much labor will the producer use to produce 50 units of the final product? What will be the total cost of producing these 50 units? b) For the production function above applies The marginal product for work MPL = K The marginal product for capital MPK = L Enter the cost-minimizing combination of capital and labor in the production of 50 units. Also enter the size of the costs. c) Write down the equation for the isocost line for the manufacturer
(A) Consider a firm in the long-run for which production depends on two inputs, labour and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 9 and r = 8, but then the price of capital decreases to r = 6. Describe the effects on labour and capital of this change in input price, represent them graphically, and explain whether this firm will optimally use more or less labour and capital. [Graph required] (B) In the long-run, if E and K were perfect complements, a wage increase would decrease the use of K. Explain why this statement is true or false.
A firm has two opportunities for a new plant location, one is in China and the other is inMexico. The firm's production function is given by q = L 0.5 K 0.5 , In China, the cost of laboris w=$15 and the cost of capital is r=$5. In Mexico, w=$10 and r=$10. The firm wants toproduce 100 units of output. Which location should the firm choose for their new plant?Explain why.Note: Please round the optimal amounts of capital and labor at each location to the nearest whole number when making your calculations.Hint: cost-minimization rule.
Consider a firm that is perfectly competitive in the market for inputs and outputs. Thefirm hires two types of workers: low-skill (high school graduates and high school dropouts) andhigh-skill (undergraduate and postgraduate degree) workers. The firm compensates high-skilledworkers at the rate wH and low-skill workers at the rate wL. It produces the output subject to aCobb-Douglas production technologyF(L,H) = (AH)α(L)β,where H - is the amount of high-skill hours, L - the amount of low-skill hours, and A - thetechnology parameter that augments the productivity of the high-skill labour. 4. In the short run, the firm cannot increase the amount of high-skill labour . Derive the1short-run demand for low-skill labour.5. What is the substitution effect of the wage increase in the short-run?6. Derive the long-run cost-minimizing demands for high- and low-skilled labour. Show thesolution to the cost-minimization problem on the graph
True or False, Explain Why 1. A production function is characterized by ? = 10 + 5L, where q is output per hour and L is labor input per hour. If workers earn $10 per hour, the marginal cost of the 5th unit of output is $10. 2. The producers’ surplus in the short-run reflects what the firms gain, while the producers ‘surplus in the log-run reflects what the input owners gain. 3. A monopoly is a price maker, thus its price can never be equal to its marginal revenue. 4. For a monopolistic competitive firm, if a government imposes a lump-sum tax on a firm, the policy will never affect its profit maximizing output and price.
please help with question below, Explain the concept of increasing-opportunity-cost with constant returns to scale. In your answer, assume that more of the labor supply is allocated to production of labor-intensive good X and more of the capital stock is allocated to capital-intensive good Y.
Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two markets
Suppose that in a perfectly competitive market, one individual firm uses twoinputs: Labor (L) and Capital (K) and it has the production function, y = √LK. The pricesof the inputs are WL = $1 and WK = $4. Assume that the number of firms in the industry can vary and all firms are identical. a. Show that the production technology exhibits constant returns to scale.b. Find the cost function of an individual firm, C(y).c. Derive and graph the average cost and marginal cost curve of an individualfirm.d. Derive and graph the long-run industry supply curve.e. If the market demand is given by D(p) = 10 − p. How many units of outputare traded in the long-run equilibrium?f. ) The government imposes a per-unit tax of $1. Find the tax incidence of thebuyer and the seller.