Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor would increase output by 1200 bottles per day (i. e. MPL = 1200). The price of a man-hour of labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally choosing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $20 per hour. How does this change the answer from part 1?

Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor would increase output by 1200 bottles per day (i. e. MPL = 1200). The price of a man-hour of labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally choosing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $20 per hour. How does this change the answer from part 1?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very…

A: The wage rate of labor (w) = GH¢2 per hour Capital is rented (r) = GH¢5 per hour, The unit price of…

Q: Consider a firm that produces cars with the following production function: q = min(aK, bL) a. Find…

A: In economics, a production function is a means of examining the relationship between input and…

Q: The following graph plots daily cost curves for a firm operating in the competitive market for air…

A: A perfectly-competitive firm produces homogenous-product. These goods(G) are substitutable. A…

Q: If the demand function for math self-help videos is given by 45 - 0.4x, and the total cost function…

A: Demand Function for math self-help videos can be written as:P = 45 - 0.4x , where P is the price ,…

Q: The Brain Bucket Company (BBC) produces helmets for winter sports. It has production facilities in…

A: Given,The production function for the Toronto facility is-The production function for the Winnipeg…

Q: A firm called a produces output Q using labor and capital according to the production function Q =…

A: We have been given the following: production function :Q = f( k,l) = 3L + 6k W = 4 R = 6

Q: f(x1, 12) = (x1 - 1)0.25x9-5.

A: We are going to use the relationship between upward sloping marginal cost curve and supply curve to…

Q: Write down the problem the car manufacturer solves to find the levels of 'K' and 'L' that minimize…

Q: Question 4 Suppose the short-run production function for a firm producing books is given by: (…

A: Given, Q=4L-0.4L2+2K PQ=10K=7.5W=15R=8

Q: Given the information from the graph below, draw the cost curve of the firm showing the minimum…

A: At Q1= 100 (L,K) = (25,25) Q2= 200, (L,K) = (50,50) Q3= 300, (L,K) = (75,75) At cost minimization…

Q: What is the marginal cost of producing the third unit of output? (Correct answer is $24)

A: Marginal cost is the additional cost that is incurred on production of an additional unit of output.…

Q: The market for smart thermostats has grown increasingly competitive. Producers of smart thermostats…

A: As we know that in the long run equilibrium the form earns only zero profit That means normal profit…

Q: As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500,…

A: The optimal level of labor and capital is given by the point where the marginal rate of technical…

Q: 1) A firm uses two inputs K and Lof capital and Labor respectively, to produce a single output Q…

Q: needs to produce 500 cups of coffee and the price of capital is 40 euro per unit and the price of…

A: A production function gives the technological relation between quantities of physical inputs and…

Q: Problem 3* A competitive firm has the following production function: f(L,K) = min {L, K}. Suppose…

A: The production function is given as w = 2r = 4

Q: K L Q 10 10 1 15 10 2 30 10 50 10 4 60 10 65 10 68 If the cost of labor is $20 per L and the cost of…

A: The firms, and businesses are the entities who are involved in the production of goods, and services…

Q: Show that the elasticity of scale for a homogeneous production function of degree k is precisely k.

A: The elasticity of scale: Elasticity of scale measures the proportionate change in output due to…

Q: a) Explain what is meant by the terms marginal cost and decreased cost in production theory, and…

A: Disclaimer :: as you posted multiple questions we are supposed to solve the first one only. Cost is…

Q: The long run cost function for the production function F(L, K) = ALºK³ is c(q, w,r) = ( 4 )a‡³…

A: Economies of scale refers to the pehnomena which describes a gradual decline in per unit costs of…

Q: You are economic consultant for Jack, who farms raw cotton in a perfectly competitive market. One…

A: a. Given: Price = $2.00 Output = 1250 Pounds TC= $7500 FC= $5625 MC= $2.00 (a) Profit = TR−TC…

Q: A Chinese high technology manufacturing firm has a production function of q=12L0.20 0.80 (based on…

A: Given Production function: q=12L0.2K0.8 ...... (1) Input prices are w=$2 and r=$8…

Q: Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are…

A: In 1970s, USA faced some economic problems automobile manufacturing industry because of competition…

Q: An economist estimated that the cost function of a single-product firm is: C(Q) = 70 + 30Q + 20Q2 +…

A: This analysis investigates the cost structure of a single-product firm based on the provided cost…

Q: You are economic consultant for Jack, who farms raw cotton in a perfectly competitive market. One…

Question

Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the
production process and finds the following. An additional machine-hour of fermentation capacity
would increase output by 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor
would increase output by 1200 bottles per day (i. e. MP₁ = 1200). The price of a man-hour of
labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 per hour.
1. Is the brewery currently minimizing its cost of production? Check using the minimization
condition.
2. It turns out, the brewery is not optimally choosing the factors of production. To lower its
production cost, which factor of production should the brewery increase and which factor
should he decrease?
3. Suppose that the price of a machine-hour of fermentation capacity rises to $20 per hour. How
does this change the answer from part 1?

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: Define Cobb-Douglas production function

VIEW

Step 2: Solution part1

VIEW

Step 3: Solution part 2 & 3

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 13 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

Ebba Kantzen says the following: "I am currently producing 10,000 pizzas per month at a total cost of $50,000. If I produce 10,001 pizzas, my total cost will rise to $50,011. Therefore, my marginal cost of producing pizzas must be increasing." ( 1.) Using the point drawing tool, indicate the point of marginal cost. Label this point "Marginal cost." 2.) Using the point drawing tool, indicate the point of average total cost. Label this point "Average total cost." Carefully follow the instructions above, and only draw the required objects. Costs(dollars per pizza) (5.95,0) MC Quantity (pizzas per month) points ATC
Suppose that a firm's production function is given by Q = 2KL, where Q is quantity of output, K is capital, and L is units of labor. Note that MPL = K and MPK-L. The price per unit of labor and capital are $30 and $50 respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 480 units of output? L = 10, K = 24 L=12, K 20 L = 20, K = 12 L = 24. K = 10
Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.
Suppose that you and a friend have started a pizza delivery business. First you had to find a shop front to make the pizzas and this costs $20,000 per year plus set up costs of $45,000 for the oven and kitchen set up. You estimate that the daily costs of labour will be $300; the ingredient cost of making a pizza is around $2.50 each and delivery is around $2 per pizza. Calculate the fixed costs of this business. If you use your combined savings to pay these costs what is the estimated implicit cost of starting the business in the first year if the interest rate is 4% per year. The government locks down the economy to prevent the spread of a deadly infectious virus, but still allows food delivery (assume that your business is one of many in a competitive market). Explain the impact of that policy on the supply, demand, equilibrium on market of pizza
5. A recent Duke graduate has opened a factory for production of textbooks in Durham. The production function is as follows f«(K;L) = K³ L Currently, she uses K = 2000 and L = 500 and the rental rates of capital and labor are w=r=$1. Now she is considering expanding her business and opening another factory in Chapel Hill. Using her microeconomic skills, she estimates that the cost function for the factory in Chapel Hill will be 3/2 C(q) = q° The firm is facing a competitive market and the price at which it can sell its output is p = $30. a. Suppose that in the short-run, both inputs in the Durham factory are fixed. What would be the profit maximizing output in the Chapel Hill factory? What would be the total output QSR of the firm? Calculate the profit Sgthat the firm will make in the short run. b. In the long run, both capital and labor are adjustable. Find the long-run cost function Ca(q) for the factory in Durham. c. Suppose that the firm wants to produce Q units in total from the…
Suppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of Labors used each hour. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?
The production function for a product is given by q = 100KL. Its marginal product functions are MPL = 100K and MPK = 100L. If the price of capital, r, is $120 per day and the price of labor, w, is $30 per day, what is the minimum cost of producing 20,000 units of output? The minimum cost of producing 20,000 units of output is $. (Round all intermediate results to 3 decimal places and enter your response rounded to two decimal places.)
The production function is y = min{x1 , x2} where x1 and x2 are the amounts of two inputsused. The price of x1 is $18 and the price of x2 is $20.a. If the firm wants to produce y = 120 units of output, how much is the (minimum)cost? b. What is the firm’s total cost function c(y)? (
The firm's production function is given as follows: qx = f(Lx, Kx). qx represents the output produced by the firm, Lx represents the labor input and Kx the capital input. In the long-run, the firm uses both inputs to produce output. An increase in the supply of capital (K) reduces the cost of capital from $6 per unit to $2 per unit. As a result, the firm's demand for the labor input (L) decreases from 200 to 120 units. Based on this information, the cross-price elasticity of labor demand is: O a. 0.50 O b.-0.25 Oc. 0.25 O d.0.75
The following table shows the capital and labor requirements for 10 different levels of production. Assuming that the price of labor (P, ) is $5 per unit and the price of capital (PK) is $9 per unit, compute and graph total cost, marginal cost, and average cost for the firm. To do this, fill in the total cost for each output level in the table below. (Enter your responses as whole numbers.) K TC 1 20 3 20 7 3 20 10 4 20 13 20 17 6. 20 23 7 20 31 3 4 5 6 i & Units of output 0 1 7 10 11 12 8. 20 41 20 53 10 20 67 LO Cost per unit ($)
Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average total cost each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.) Average Total Cost (Dollars per bike) Number of Factories O = 100 Q = 200 Q = 300 Q = 400 Q = 500 O = 600 1 520 400 320 400 560 800 660 480 320 320 480 660 800 560 400 320 400 520 Suppose Ike's Bikes is currently producing 500 bikes per month in its only factory. Its short-run average total cost is $ per bike. Suppose Ike's Bikes is expecting to produce 500 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using On the following graph, plot the three short-run average total cost curves (SRATC) for Ike's Bikes from the previous…
2. A production process using two inputs, labor and capital is Q = 5LK where Q is output per day. MPK = 5L and MPL = 5K. The wage (w) = $150 per hour and (r) = $1,000 per hour. Determine the least cost combination of K and L when the desired output is 1,000 What is the minimum cost of producing 1,000 per day?