Suppose a firm producing wood burning stoves has the following production functionQ(K, L) = 4K¹/2 [1/2Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantityof stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2.a)b)Assume that K=9 in the short run. Draw the production function and calculate themarginal products of L as L changes from L= 1 to L= 6.What does an isoquant curve show? Draw the graph of a production isoquantrepresenting input combinations that will produce 8 units of output. c)d)e)h)Define the marginal rate of technical substitution. How would you represent it inthe previous graph?Does this production function exhibit increasing, decreasing or constant returns toscale?Suppose that the market for wood burning stoves is also perfectly competitive. Firms in themarket are identical and each firm has a total cost function: TC(q) = 3q³ − 9q² + 15q + 20.q is given in number of stoves and P in hundreds of pounds.f)If the equilibrium price in the wood burning stoves is equal to £15, what is thequantity of stoves supplied by a firm?What is the profit made by a firm?Find the equation for the average variable cost of a firm. Calculate the shutdownprice of a firm. What does it represent?Comment about the situation of the firm based on your answer in g) and h).Given your answer in g), comment on what is likely to happen on the market in thelong-run. Illustrate your answer with graphs.i)j)Suppose the firm is producing Q = 48 stoves using 9 units of labour and 16 ofcapital. Is the firm producing its current level of output at the minimum cost? Ifnot, what should the firm do?

Production function is the mathematical expression of the amount of output a system or firm produces…

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K ¹/21/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K ¹/21/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.1P

See similar textbooks

Related questions

Q: A firm can manufacture a product according to the production function:Q=F(K,L)=K^(3/4)…

A: The production function is given as: The average product of labor is calculated by dividing the…

Q: Given the production function q = 1.37LK, what is the marginal product of labor? A) 1.37 B) 0 C)…

A: Marginal product of labor is the additional output produced by employing an additional worker

Q: A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a)…

A: We are going to calculate average product of labour and marginal product of labour

Q: A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a)…

A: Answer to the question is as follows :

Q: A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP (1/3)*LN(1/5) per…

A: The production function is the mathematical relationship between the output produced and the inputs…

Q: Suppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of…

A: The production function shows the relationship between the factors of production to be used and the…

Q: Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an…

A: The Cobb-Douglas production function is a mathematical equation that represents the relationship…

Q: 1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship…

Q: Consider a production function of two inputs, labor and capital given by Q=LK. Let w =5 and r = 1,…

A: Production function refers to the function which shows the relationship between the final output and…

Q: A firm has the following production function: q = KL, where q is output, K is capital and L is…

A: A firm has production function: q = KL, The price of a unit of capital is $1,000 The price of a…

Q: A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is…

A: Marginal product is the amount by which production of a commodity changes from employing more unit…

Q: c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number…

A: The production function shows the connection between inputs such as land, labor capital, and…

Q: A firm produces output according to a production function: Q=RK,L) = min [4K,4L). a. How much output…

A: The production function determines all the input bundles that produce the same output level.The…

Q: Q = L1/2 K1/2 They have 16 units of capital (which is fixed in the short-run). The unit cost of…

A: The production function refers to the functional relationship between input and output, which…

Q: 1. A firm can manufacture a product according to the production function Q = F(K, L) = K³/4L¹/4 a.…

A: Q = K3/4L1/4

Q: A firm can manufacture a product according to the production function Q = F(K, L) = K3/4 L1/4 a.…

Q: Asap A firm has the following linear production function: Q = 6K + 9L The firm currently owns…

A: Answer: Given, Production function: Q=6K+9L K = 10 units L = 30 units (A). Marginal product of…

Q: A firm can manufacture a product according to the production function Q=3K1/2L1/2, and capital is…

A: When capital is fixed at 4, the production function in terms of labor(L) is;…

Q: A company can manufacture a product according to the production function Q=3K1/2L1/2, and capital is…

A: The cost of production is delineated in social science because the expenses spent to urge the…

Q: A firm has the production function X = LK (X = output, L = labour, K = capital); labour and capital…

A: Production is a critical component of economics as it adds value to the economy by putting labor to…

Q: A firm's production function is q = 26x^0.33y^0.67, where x and y are the amounts of factors x and y…

A: 1. Minimize Unit Costs:Unit cost (C) is defined as the total cost of production (Px + Py) divided by…

Q: Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total…

A: Production and cost function: The production function determines all the input bundles that produce…

Q: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the…

A: The Cobb-Douglas production function is a widely used mathematical representation of production…

Q: Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The…

A: (a) : 1. Cost-minimizing quantity of labor (L*): MPL = w KM = 5 L* = 5 / K2. Cost-minimizing…

Q: n the short run, a firm cannot vary its capital and operates with K = 9. It can, however, vary the…

A: Production function: It shows a relation between physical output and input of a production process.

Q: Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25…

A: Technical Rate of Substitution (TRS) is the amount that must be decreased from one input (capital)…

Q: If x₁ = x₂ = 16, the marginal product of input 1 is two inputs is w₁ = 2 and ₂ = 1. When ₁ is…

A: Production function shows the functional relationship between the output and inputs. The production…

Q: Suppose that the production function for Hannah and Sam's home remodeling business is Q=FL.K)…

A: The link between the quantity of productive inputs (such as labor and capital) utilized and the…

Q: The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is…

A: The production function is:q = 10*K0.5*L0.5The cost function (C) with two inputs capital (K) and…

Q: Suppose that a firm’s production function is Q = 2L0.5 + 3K0.5. The cost of a unit of labour is R2…

A: Given Production function Q=2L0.5 +3K0.5 ........ (1) cost of labor w= 2 Cost of capital r= 1…

Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

Suppose a firm producing wood burning stoves has the following production function
Q(K, L) = 4K¹/2 [1/2
Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity
of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2.
a)
b)
Assume that K=9 in the short run. Draw the production function and calculate the
marginal products of L as L changes from L= 1 to L= 6.
What does an isoquant curve show? Draw the graph of a production isoquant
representing input combinations that will produce 8 units of output.

c)
d)
e)
h)
Define the marginal rate of technical substitution. How would you represent it in
the previous graph?
Does this production function exhibit increasing, decreasing or constant returns to
scale?
Suppose that the market for wood burning stoves is also perfectly competitive. Firms in the
market are identical and each firm has a total cost function: TC(q) = 3q³ − 9q² + 15q + 20.
q is given in number of stoves and P in hundreds of pounds.
f)
If the equilibrium price in the wood burning stoves is equal to £15, what is the
quantity of stoves supplied by a firm?
What is the profit made by a firm?
Find the equation for the average variable cost of a firm. Calculate the shutdown
price of a firm. What does it represent?
Comment about the situation of the firm based on your answer in g) and h).
Given your answer in g), comment on what is likely to happen on the market in the
long-run. Illustrate your answer with graphs.
i)
j)
Suppose the firm is producing Q = 48 stoves using 9 units of labour and 16 of
capital. Is the firm producing its current level of output at the minimum cost? If
not, what should the firm do?

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: Introduction

VIEW

Step 2: Illustration of production function

VIEW

Solution

VIEW

Step 3: Understanding Isoquant

VIEW

Step 4: Understanding MRTS

VIEW

Step 5: Calculation of returns to scale

VIEW

Step 6: Calculating efficient allocation

VIEW

Step 7: Calculation of market equilibrium

VIEW

Step 8: Calculation of Profit

VIEW

Step 9: Calculation of average variable cost and shutdown point.

VIEW

Step 10: Analysis of long-run production

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 11 steps with 3 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

What is the difference between a fixed input and a variable input?
1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?
6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?
Frisbees are produced according to the production function q = 2K+Lwhere q =output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquantd defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant.
The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
Please give exact answer step by step and take a like
2) The general Cobb-Douglas production function for two inputs is given by: q = f (k, l) = AKªL® where 0 0, f¡ > 0, frk 0. b.) Show that = a and ɛg,i Eq,k B (Note that ɛ's are elasticities). || C.) Show that, for this Cobb-Douglas function, production is CRS if a + ß = 1.
6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
Please answer fast and Arjent please
Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…
The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? How much will hiring these inputs cost them?