A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K1/2 L1/2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?

A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K1/2 L1/2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Proudction Costs

Section: Chapter Questions

Problem 2SQ

See similar textbooks

Related questions

Q: Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is…

A: The firm maximizes profit by hiring the number of workers at a point where MPE = w/p

Q: A firm in a competitive marketplace employs 10 workers at a wage rate of $20 per hour, and 10 units…

A: Cost Minimization Producers utilize cost minimization as a fundamental guideline to identify what…

Q: Assume a firm incurs overall labor costs of $22 per hour- which includes wages and training costs.…

A: Labor Cost = $22/hr Training cost = $160/hr Wage = $20/hr G = 1/Workers

Q: Consider the two production functions: .Fixed proportions: q = [min(k, l)]* ii. Perfect substitutes:…

A: Fixed proportions: q = [min (k, l)]s Perfect substitutes: q = (k + l)s

Q: The production function of a given item is Q = 10(L^½)(K^½) and the factor prices are equal to $20…

Q: Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is…

A: A production function represents the relationship between the quantities of factors of production to…

Q: A widget manufacturer has a production function of the form q= VLK. If the wage rate (w) is $4 and…

A: production function q=Lk,w=4 r=1returns to scorelet y=Lk=f(k,L)solving all factors of production by…

Q: Consider a firm for which production depends on two normal inputs, labor and capital, with prices w…

A: (a) The change effect reflects the company's change in the input combinatioñ due to the change in…

Q: Suppose in a purely competitive product market, price is $10. If a firm's production function is…

A: Given production function Q=L0.4K0.6 .........(1) Let w be the wage rate and r is cost of…

Q: Suppose the marginal product of labor equals 1/L. If the wage is $15 per unit of labor, what is the…

A: Marginal Product of Labor (MPL): - it is the change in total production due to the employment of an…

Q: Given prices for the two inputs as w1 = 1, w2 = 2, find the cost function of the (attached)…

A: Answer to the question is as follows:

Q: Suppose that the production function of the firm is: Q = 100L1/2.K1/2 K= 100, P = $1, w = $30 and r…

A: Given, Q = 100L12K12K= 100 P = $1 w = $30r = $40.

Q: Suppose the firm is hiring labor and capital and that the ratio of marginal products of the two…

A: Marginal product: It refers to the input, i.e. labor which is defined as an extra output that…

Q: The market for drones is perfectly competitive. Labor is the only variable input. The fixed cost is…

A: Quantity of Labor (L) Quantity of Output Wage Rate (WR) Total Cost (L*WR) Marginal Cost (TCn -TCn-1)…

Q: A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The production function of a competitive firm is described by the equation y = 1/2G1/2 2.x6x. The…

A: y = 2x1126x212 p1 = $3 p2 = $4To find Marginal Product of good 1 (MP1) differentiate y with…

Q: Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short…

A: Given, y= f(x1,x2)=x11/3x21/3 Amount of x2 = 216

Q: The short run production function is q = 10*L. The wage rate is $10 per unit of labor, then AVC:

A: AVC is total cost divided by output.

Q: The production function shows: a. The level of output as a function of the quantity of inputs.…

A: The markets are considered to be place where the meeting, and interaction of the buyers of various…

Q: A manager hires labor and rents capital equipment in a very competitive market. Currently the wage…

A: Given wage rate (w) = $12Capital rent (r) = $8Marginal product of labor (MPL) = 60 unitsMarginal…

Q: Consider the long-run cost minimisation problem, with L on the horizontal axis and K on the vertical…

A: A firm will minimise its cost at a point where marginal rate of technical substitution is equal to…

Q: Assume a firm incurs overall labor costs of $22 per hour - which includes wages and training costs.…

A: Labor market equilibrium is getting where the labor demand and labor supply intersect with each…

Q: For a competitive firm; production function, market price and unit costs for capital and labour are…

A: Given, Q(K,L) = K1/2L1/4 and p = 8, r =0.1 , w = 10 Input demand for Labor L = f (w,r,p) Input…

Q: Suppose that the production function of the firm is: Q = 100L1/2.K1/2 K= 100, P = $1, w =$50. and…

A: Answer: Given, Production function: Q=100L12K12 K=100 P=$1 w=$50 r=$40 Calculation: To find the…

Q: Determine whether each of the following is an explicit cost or an implicit cost :a. Payments for…

A: The total cost incurred by a firm operating in a market includes fixed costs and variable costs.…

Q: Suppose a firm’s production function is q= 2L+ 5K, the wage is w= 4, and the rental rate of capital…

A: Cost function is the total cost incurred to produce a good. It is the total sum of cost incurred on…

Q: f q = 4 lnL and the good is sold for $10 then if the wage rate is $5 the number of units of labor…

Q: firm has the production function q=L2K The wage rate is w=55 and the rental rate is r=44. In the…

A: Production function, in financial aspects, condition that communicates the connection between the…

Q: A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent…

A: Production function is convex at the first then after the inflexion point becomes concave. An…

Q: A firm´s production function is given by: y = x² where y is the total output per time period, and x…

Q: A competitive firm produces output using three fixed inputs and one variable input. The firm’s…

A: A competitive firm minimizes cost by employing the number of input where its marginal product is…

Q: Consider a firm with the production function q = L}K* The firm faces a wage rate of w = 20 and a…

A: The given production function is a ‘Cobb-Douglas’ function where the producer uses both labor(L) and…

Q: To produce a recorded DVD, a firm uses one blank disk D and the services of a recording machine M…

A: Given information Production function Q = min{D, M} Here 1 DVD is produced by using 1 blank disk…

Q: Suppose that a firm has a short-run cost function C(q) = q2 +1. Part a Find the short-run supply…

A: In a market, a firm’s cost function can provide information about different types of costs such as…

Q: Show your work whenever possible. A firm has the following production function. Q=K.√L the rent…

A: In the production of goods and services, various factors of production or inputs are used in…

Q: Suppose that a firm had a production function given by: q=LK () is $5. The wage rate (w) is $10 and…

A: In economics, a production function gives the technological relation between quantities of physical…

Q: Suppose that the production function of the firm is: Q = 100L1/2 . K1/2 K= 100, P = $1, w = $50 and…

A: production function is referred to the relation of the number of inputs which a firm uses with its…

Q: Assume a firm has the following short-run production function: q(L) = L+6L2-1/2L3 If this firm is…

A: Answer in step 2

Q: Suppose a competitive firm is paying a wage of $12 an hour and sells its product at $3 per unit.…

A: Labor demand refers to the amount of labor-hour that a employer is willing to hire. Worker demand is…

Q: A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L* where K and…

A: Since, the question has multiple sub parts, we will be answering the first three parts for you. If…

Q: Maria's Umbrellas has a production function given by Q = L0.5K0.5. The wage (W) is $80 per day and…

A: The link between the quantity of productive inputs (such as labour and capital) used and the amount…

Q: The production function of a competitive firm is described by the equation y = 2x11/2 6x21/2. The…

A: We are going to find cost structure in terms of Q and then find Marginal Cost.

Q: What is the cheapest way of producing 850 units of output if a firm operates with the production…

A: It is given that;

Q: In the short run, the owner of a firm should continue to hire additional units of labor until: a.…

A: In the short run, the equilibrium condition is wage equals the marginal revenue product of the…

Q: Suppose the production function is q= f (L,K)=2L+4K . If wages are set at w=$2 and the price of…

A: Answer- Given in the question- q= f (L,K)=2L+4K If wages are set at w=$2 and the price of capital is…

Q: A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α) 0<α < 1 is a…

A: Production Function: q = LαK1-α In the short run, K = 1. Therefore: q = Lα⇒L = q1α Total Cost: TC =…

Q: Suppose you have following production function for your firm :q = 2x,"x, where x, > 0, x, >0 and a ±…

A: Production function: q = λx1ax21-a ..........(1) Input price x1 = w and x2 = r The marginal…

Question

A firm produces output that can be sold at a price of $10. The production function is given by

Q = F(K, L) = K^1/2 L^1/2

If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

A firm produces output that can be sold at a price of $10. The production function is given by Q = F(K, L) = K2L!2 If capital is fixed at 1 unit in the short run, how much labor should the firm employ to max- imize profits if the wage rate is $2?
Suppose that a firm has the following production function: q = 2L + K. The wage for a $10 per hour and the rental rate of capital is r = worker is w $10 per hour. In the short run the firm amount of capital is fixed at K = 20 units. If the firm's goal is to minimize their cost of producing 100 units, then in the short run they will hire units of labor and in the long run they will hire units of labor. (Round answers to two decimals if necessary.)
A short run production function of a competitive firm is given by Y=6L^(2/3) where Y represents the units of output while L is the labour required. If P = 3 and W = 6. How many units of L will the firm hire?
The production function of a competitive firm is described by the equation y = 2x11/2 6x21/2. The factor prices are p1 = $3 and p2 = $4 and the firm can hire as much of either factor it wants at these prices. What is the firm’s marginal cost?
Suppose the firm short run production function is a quadratic one in the form: Q = 2L+ 0.25 L2, the firm hires any number of workers at a wage of $40/day, and sell any quantity of its output at a price of $4. Find how many workers should this firm hire to maximize profits.
A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with q
A firm operates in the short run with the production function Q = 10 K0.5 L 0.5, where Q is output, K is capital, and L is labor. The price of capital is $100 per unit, and the wage rate is $50 per unit of labor. How many units of capital and labor should the firm use to minimize its total cost while producing 400 units of output?
Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r
A plant's production function is Q = 2KL. For this production function, MPx = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at K = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.
For a short run production function q=10lnL if L=5 and wage 3, more workers will be hired if the price at which the output can be sold is more than.......
A firm operates in a perfectly competitive output market and a perfectly competitive input market. The production function for the firm is: f(N, K) = N K The price of labour is $10, and price capital $20. If the firm needed to produce 100 units, how much capital and how much labour should they use in the long-run?
1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes