(04.Suppose we are given (he constant returns to scale (CES) production functionq= { ßa + aa }1/aa. Show that the marginal product of Beta is (g/B) and marginal product of Alpha(q/a)**b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a)1-a

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

Q4.Suppose we are given the constant returns to scale (CES) production function q={ßa+aa }1/a a. Show that the marginal product of Beta is (q/B) and marginal product of Alpha (q/a)¹-2 b. Show that RTS = (a/B)¹; Hence or otherwise show that the 6 = 1-2 =1/(1-a)

Q4.Suppose we are given the constant returns to scale (CES) production function q={ßa+aa }1/a a. Show that the marginal product of Beta is (q/B) and marginal product of Alpha (q/a)¹-2 b. Show that RTS = (a/B)¹; Hence or otherwise show that the 6 = 1-2 =1/(1-a)

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter8: Production And Costs

Section: Chapter Questions

Problem 2WNG

See similar textbooks

Related questions

Q: Consider the Mortensen-Pissarides model described in the lecture. Now suppose that an unemployed…

A: Unemployment refers to a situation in which individuals who are willing and able to work are unable…

Q: a. Define the concept of equilibrium in the foreign exchange market, from an Australian perspective,…

A: The term "equilibrium" in the context of the foreign exchange market describes a situation in which…

Q: Which of the following changes will have the smallest impact on the aggregated demand in the…

A: Government Spending(G): Government spending refers to the expenditures made by the government on…

Q: Let X = 9, Y = 6 and Z = 14. If Firm A chooses sell, then in the subgame, B should choose if…

A: The best response strategy is defined as the strategy which gives you the maximum payoff , given the…

Q: With all other exogenous variables at their original levels, suppose the Central Bank attempts to…

A: Expansionary monetary policy involves a series of measures implemented by a central bank to boost…

Q: A company wants to buy a production device for their new factory. They have two alternatives, whose…

A: To determine the best alternative based on the payback periods, we need to calculate the payback…

Q: Consumption function: C = 60+ 0.75Y * Investment: 1 = 90 • Government spending: G = 52 • Net taxes:…

A: Aggregate demand refers to the total demand for commodities and services made by all the economic…

Q: In a world of zero transportation costs, no trade barriers, and significant differences between…

A: International trade implies the exchange of goods, services, and capital between different countries…

Q: Overview: The US government is reviewing the topic of a cap-and-trade system for carbon emissions,…

A: To: Secretary of State From: XYZ Date: July 24, 2023 Subject: Recommendation on Cap-and-Trade…

Q: How do sales taxes typically apply in a business environment?

A: Sales tax is a consumption tax imposed by the government on the sale of goods and services. It is…

Q: 6. Total planned expenditure (equals income) is 15,000, - cr = 600, the marginal propensi to consume…

Q: Find the simple interest. Principal Rate Time in Months $10000 4% 3

A: Present value is the value of investment in today's dollar. Future value is the value of investment…

Q: _____ theories of judgment and decision making describe how people should behave, as opposed to how…

A: In this case, we have to discuss the term normative, objective, unbounded and legitimate theories of…

Q: Navigate through the various pricing models used in any market economy

A: In a marketplace economy, organizations use various pricing models to set the charges of their items…

Q: Discuss value-based pricing in a market economy

A: A market economy, also called a free-market economy or capitalist economy, is an economic system…

Q: Consider the following 2-player game with incomplete information U D L (0. y) (-1, y) R (1, 2) (0,0)…

A: According to the game theory concept's BNE, each player's strategy is optimal given their personal…

Q: Krysel Inc. is expecting a new project to begin producing cash flows at the end of this year. They…

A: It can be defined as the quantitative value or worth of an investment, asset, or any kind of project…

Q: Fast-and-frugal heuristics are hypotheses about how people ____ make decisions. 1. Normatively 2.…

A: Behavioral economics brings together psychological and economic ideas in order in order to better…

Q: Read Kiyotaki (1998). Consider the model in section 2 of the paper. Suppose there is no borrowing…

A: The net interest rate refers to the effective interest rate earned or paid on financial assets or…

Q: Suppose that a particular industry has a four firm concentration ratio of 45 and a herfindaji index…

A: Business economics is concerned with the research and analysis of business finances using economic…

Q: 1. Using the following information, calculate total utility and marginal utility. a. Plot the total…

A: The utility is the wants satisfying power of a product. Total utility is the total amount of…

Q: 2) Consider the following 2-player, simultaneous move static game summarized by the normal orm…

A: Dominated strategy refers to the strategy which is less attractive strategy relative to other…

Q: inflation rate in 2018? 1) 2% O2) 4% 3) 6%

A: It can b defined as a method that helps measure the change (increase or decrease) in a specific…

Q: Consider an economy with three people and two goods: private good (x) and public good (y). Suppose…

A: Public Goods :- Public goods which are non-rivalious and non-exhaustive in nature and total amount…

Q: Given this information, how much is the MP for worker (L) for worker 2 and 3. P Q 15 05 and 5 O 35…

A: PQTR(PxQ) MR(dTR/dQ)MP(dQ/dL)MRP(PxMP) FP(L)500---0584040/8 =58/1 = 8 4015157535/7 = 5735252010025/5…

Q: You sold $425,000 this year, 15% less than last year. Rest of market sales dropped 20% to $720,000…

A: Given: Our firm sold $425,000,000 , 15% lower than last yearThe rest of firms sold $720,000,000 ,…

Q: The table below shows nominal and real GDP figures for a hypothetical economy, Nebula. Nominal GDP…

A: We have given the data of nominal GDP and real GDP with GDP deflator.The GDP deflator is calculated…

Q: Complete the following table by calculating the negative tax and total after-tax income for each…

A: It can be defined as a policy of the government in which Any individual or family in the economy has…

Q: shows a consumer's tradeoff between safety-related effort and their expected loss before and after…

A: The trade-off is one of the basic principles of economics. The event of foregoing one opportunity…

Q: Write the goods market equilibrium conditions/equations and draw the graph of market equilibrium.

A: In an open economy, the goods market equilibrium conditions are based on the equivalency of…

Q: When firms sell highly differentiated consumer goods, what is one significant cost all firms are…

A: a. advertising expensesWhen firms sell highly differentiated consumer goods, one significant cost…

Q: 1.Factory does not install scrubber,Farmer uses south field Crop Damage ($)= 120 Farmer cost ($)=0…

A: Willingness to pay (WTP) is a concept used in economics and decision-making to measure the maximum…

Q: 4. Refer to Figure 13.1. The upper curve (SS) in the figure represents the Price and Costs ($) 10 8…

A: When there is a loss or benefit to society (third party) without being directly involved in it.

Q: 5. The Role of Government: Quota - Quantity Regulation Smoking imposes health risks to others and…

A: An externality, in economics, refers to a side effect or consequence of an economic activity that…

Q: Workers come in many different types, or productivities. The productivity of a worker is given by…

A: In terms of economics, productivity refers to the ratio of output to input in a production process.…

Q: Pu P3 P₂ P₁ Qi Q₂ Q Q4 MR MSC тре D a. What price and quantity will the firm in the diagram above…

A: In economics, MSC, MPC, and MR are important concepts that relate to the study of production, costs,…

Q: What payment is required at the beginning of each month for 5 years to repay a loan of $25 000.00 at…

A: Compounding refers to the process of charging interest on the principal amount as well as on the…

Q: E MR S D What point reflects the price that a monopolist would charge? (letter) ATC AV C A/ What…

A: “Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Please continue to solve from Part d to Part e. Thank you

A: Time series data is a type of data where observations are recorded at regular time intervals, such…

Q: Suppose the production process of a particular good creates a negative externality such as…

A: When a production process creates a negative externality including pollution, the cost of producing…

Q: Equilibrium is reached in a market because both consumers and producers have an incentive to change…

A: Equilibrium refers to a situation at which the demand is equal to the supply in a market. There is…

Q: do you believe that the Campiness present in Batman 1989 was intentional or unintentional?

A: In assessing the campiness in the 1989 film "Batman," it is important to consider whether this…

Q: QUESTION 12 a firm operating in a purely competitive market $ 40 36 32 28 24 20 16 12 8 4 0 K 0 4 8…

A: In perfect competition, There exists a large number of buyers and sellers. There is no barriers to…

Q: Currently, the U.S. has a total consumption of $10,000,000, savings of $4,000,000, tax revenues of…

A: Aggregate demand refers to the total demand for commodities and services made by all the economic…

Q: F 180= FS 160 F4 140 = F3 120= F² 110 F1 O 1 Figure 1 Production Possibilities Curve (PPC) --t V W…

A: Production Possibility Curve of PPC shows the different combinations of two goods that can be…

Q: Given the following data, calculate Net Domestic Product (NDP) at market prices: Gross National…

A: Net Domestic Product (NDP) is an economic indicator that measures the total value of all goods and…

Q: Suppose a small country, Country X, is considering implementing a Carbon Tax to address…

A: A Carbon tax is a fee imposed on the carbon content of fuels.The tax is levied to reduce carbon…

Q: Using the first-order conditions of this problem with respect to C₁, C₂ and s₁, (i.e. the partial…

A: For the above question let us first derive the lifetime budget constraint : Budget constraint for…

Q: (percent) 10. Referring to the graph above, a movement from point F to point G might represent

A: Above graph depicts rate of interest on vertical axis and inflation rate on horizontal axis . There…

Q: What are the needs of the industry price leaders? a. market demand. b. market demand plus the demand…

A: Price leadership happens when a dominant firm within an industry holds enough sway to influence the…

Question

(04.Suppose we are given (he constant returns to scale (CES) production function
q= { ßa + aa }1/a
a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha
(q/a)**
b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a)
1-a

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Define production function and productivity:

VIEW

Step 2: Calculate marginal products:

VIEW

Step 3: Calculate RTS:

VIEW

Solution

VIEW

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

What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?
In choosing a production technology, how will firms react if one input becomes relatively more expensive?
What is the difference between a fixed input and a variable input?
12. Which of the following production function shows decreasing returns to scale? (a) f(r) = min{x1, 12}. 1/4 (b) f(z) = xỉ + x}/2 1/4 1/2 (c) f(x) = r1 + xj"x (d) f(x) = VE +a3.
Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…
What is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?
4:34 D *3 all 100% I 2. 3 When the inputs price ratio (slope of cost line) is greater than the MRTS, (MPK/PK > MPL/PL) the producer should use .. to minimize the cost. A More labar C Mare labor and more capital B More Capital D| None of the above 4 The optimal production method A maximizes output regardiess of cost C minimizes the normal rate of return B| maximizes inputs. Dminimizes cost 5. Refer to the information provided in the following figure, If this firm's cost of labor is $10 per unit, and the isocost line represents a total cost 2000. How much is the cost of capital per unit? 100 q-300 -200 -100 200 Units of labor Linits of capital
Suppose that a food manufacturing company produces two goods, A and B, using the same plant and labor. The total cost of producing A and B is give by: (in the picture) Is this total cost function consistent with the present of increasing or decreasing returnsto scale
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.
Suppose that the dollar cost of producing x appliances is c(x) = 1000 + 70x-0.1x². a. Find the average cost per appliance of producing the first 100 appliances. b. Find the marginal cost when 100 appliances are produced. c. Show that the marginal cost when 100 appliances are produced is approximately the cost of producing one more appliance after the first 100 have been made, by calculating the latter cost directly. CUCKO The average cost per appliance of producing the first 100 appliances is $ (Round to the nearest cent as needed.) /appliance.
Saved Suppose a firm has only three possible plant-size options, represented by the ATC curves shown in the figure. What plant size will the firm choose in producing (a) 50, (b) 130, (c) 160, and (d) 250 units of output? Average Costs 50 40 30 ATC ATC ATC, 20 10 130 160 250 50 30 60 90 120 150 180 210 240 270 300 Output a. 50 units of output: (Click to select) b. 130 units of output: (Click to select) c. 160 units of output: (Click to select) d. 250 units of output: (Click to select) ATC
Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.