The countries of Aloha and Biki both have the production function Y = K^{1/3} L^{2/3} (a) Does...
Question:
The countries of Aloha and Biki both have the production function
{eq}Y = K^{1/3}L^{2/3} {/eq}
(a) Does this production function have constant returns to scale? Show why or why not.
(b) Derive the per-worker production function (i.e. y = f(k))
(c) Draw a Solow diagram for Aloha and show their steady state. Now, suppose that the depreciation rate of capital, {eq}\delta {/eq} increases due to inadequate maintenance of their roads. Show the new steady state.
(d) Suppose that the country of Aloha has a higher savings rate than Bikini. Draw a Solow diagram and show the steady state of both countries on the same diagram. Which country will be richer in terms of income per capita?
Production:
The term production in economics can be defined as a process by which the raw materials and other valuable inputs are utilized to manufacture a final product for the market by using production factors like labor, capital and entrepreneurship.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answera.
No, the given function is not a constant return to scale rather it is a Cobb Douglas production function. This is so because an increase in the...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
What is Economic Growth? - Definition, Theory & Impact
from
Chapter 8 / Lesson 6
55K
Learn all about economic growth. Read a detailed definition of economic growth, learn the theories of economic growth, and see the importance of this concept.
Related to this Question
- The countries of Aloha and Bikini both have the production function Y=K^{1/3}L^{2/3}. (A) Does this production function have constant returns to scale? Show why or why not. (B) Derive the per-worker
- Suppose a country has the following production function: Y = F(K, L) = K0.4L0.6. Does this production function have constant returns to scale? Explain.
- Suppose the production function for a country is given by Y = F(K, L) = K0.4L0.4. Does this production function have constant returns to scale? Explain.
- Country A and country B both have the production function: Y = F (K, L) = K^0.5 L^0.6 a) Does this production function have constant returns to scale? Explain
- Country A and country B both have the production function Y = F(K,L) = K^{1/3} L^{2/3}. a) Does this production function have constant returns to scale? Explain. b) What is the per-worker production f
- Country A and country B both have the production function Y = F(K,L) = K^{1/3}L^{2/3}. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production
- Country A and country B both have the production function Y = F(K,L) = K^{1/3}L^{2/3}. (a) Does this production function have constant returns to scale? Explain. (b) What is the per-worker producti
- Suppose we have the following production function: Y = F (K,L) = A(2K + 3L). Does this function exhibit constant returns to scale? Why or why not?
- a) Suppose two countries have the following production function: Y=F(K, L)=K^(0.3)L^(0.7). b) Is this production function constant returns to scale? Express the above production function in per worker
- State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale or constant returns to scale, briefly explain.
- Why is it sensible to assume that the production function exhibits constant returns to scale and diminishing returns to capital?
- Does the production function q=100L- {50}/{K} exhibit increasing, decreasing, or constant returns to scale? This production function exhibits ____ returns to scale.
- Given the following production functions, test if they exhibit constant returns to scale. Be sure to mathematically prove your answer and show your work. A) Y = 2K + 15L B) Y = 2(K + L) ^0.5 C)
- Suppose you have two production functions: (i) y = A(K + L) (ii) y = A + (K + L) Demonstrate how one function is a constant return to scale and the other is not.
- Which of the following production functions exhibit constant returns to scale? (a) F(K, L) = KL/10 (b) F(K, L) = KL (c) F(K, L) = (KL)^2 (d) F(K, L) = K + L
- Determine whether the production function T(L, K)=10L+2K, yields an increasing or decreasing returns to scale or a constant returns to scale.
- What are the characteristics of a unique long-run equilibrium, and why is it not possible to find given a production function exhibiting constant returns to scale over a given range?
- Determine which of the following production functions exhibits constant returns to scale (CRS). a) Y=0.5K+0.3L b) Y=(K L)^1/2 c) Y=min{K,0.3 L} d) Y=K^0.3 L^0.5
- Let a production function exist such that Q=(K0.30 L0.75) a) Does this production function exhibit Increasing, Decreasing or Constant Returns to Scale? Explain what your answer means and how you know.
- Define returns to scale. Ascertain whether the given production function exhibit constant, diminishing, or increasing returns to scale.
- Suppose f(L, K) = K^2 + LK + L^1/2 K^1/2. Does this production function exhibit increasing, decreasing or constant returns to scale? Show your work.
- What are the returns of scale for this production function: Qs = 2L^{0.3}K^{0.8} and why?
- Solow-function transformations Y_t=K_{t}^{a}(A_tL_t)^{1-a} K_{t+1}=(1-delta)K_t+I_t I_t=S_t=sY_t a. Show that the production function above has returns to scale. b. Transform the production function i
- The production function f(K,L) = (max\begin{Bmatrix} K,L \end{Bmatrix})^\frac{1}{2} exhibits... \\ A. Decreasing returns to scale B. Constant returns to scale C. Increasing returns to scale D. None of the above
- Given the production function q = 10K_{a}L^{B}, show that this exhibits constant returns to scale if a+B = 1.
- Suppose you have two production functions where A is constant total factor productivity: (i) y = A(K + L), (ii) y = A + (K + L) Show/demonstrate that only one is a constant returns to scale production function. Also, show/demonstrate that the other
- Does the production function: q = 100L - 20/k exhibit increasing, decreasing, or constant returns to scale?
- A production function Y=F(K,L) exhibits constant, decreasing, increasing returns to scale if for some positive number a, say a=2, we have: Constant returns: F(aK,aL)=aF(K,L)
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale.
- Consider a production function of the form Y = AF (K, N, Z), where Z is a measure of natural resources used in production. Assume this production function has constant returns to scale and diminishing
- Assume that the aggregate production function for an economy is described by: where 0 < a < 1. a. Show the production function has the property of constant returns to scale. b. Obtain the per capita
- The production function q = 22K^{0.7}L^{0.1} exhibits A. increasing returns to scale. B. constant returns to scale. C. unknown returns to scale because the exponents are not equal. D. decreasing returns to scale.
- Consider the following production function: q = 4LK. Which term describes this production function's returns to scale? A. increasing returns to scale B. decreasing returns to scale C. constant returns to scale
- A production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L) , where K is capital and L
- Explain the meaning of the aggregate production function. What are the constant returns to scale in relation to the aggregate production function?
- Show whether the following production functions exhibit constant returns to scale, decreasing returnsto scale or increasing returns to scale. Please do not just state your answer, but show mathematica
- Which of the following production functions exhibits constant returns to scale? A. F(K, L) = K^{1/3}L^{1/3} B. F(K, L) = 0.5KL C. F(K, L) = K^{1/2}L^{1/2} D. F(K, L) = K^2L
- Show mathematically that the following Cobb Douglas production function has constant returns to scale. F(K,L) = AK^(2/3)L^(1/3)
- Q10. Show mathematically that the following Cobb-Douglas production function has constant returns to scale. F(K,L)= AK^(2/3)L^(1/3)
- Do the following production functions exhibit decreasing, constant, or increasing returns to scale? Show calculations to justify your answers. (a) Q = 0.5KL (b) Q = 2K + 3L (c) Q = L + L1/2K1/2 + K
- Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z is greater than 0: F(z \cdot K, z \cdot L) = zF(K,L) (1) For example, f
- The production function Y = (X^2)*(X^{0.5}) has returns to scale. a. increasing b. marginal c. decreasing d. constant
- Which of the following four production functions exhibit constant returns to scale? In each case, y is output and K and L are inputs. (Select all that apply.) a. y = K1/2L1/3 b. y = 3K1/2L1/2 c. y = K1/2 + L1/2 d. y = 2K + 3L
- Determine whether the following production function have increasing, decreasing or constant returns to scale. a. Q=0.001M+50,000 b. Q=15K+0.5KL+30L
- Assume a production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L), where K is capital
- Consider the production function Y=\frac{X-500}{20}, where Y is output and X represents inputs. Graph this production function. Does it display decreasing, constant, or increasing returns to scale?
- Consider the CES production function. This production function exhibits A. constant returns to scale. B. decreasing returns to scale. C. increasing returns to scale. D. either decreasing or constant returns to scale, but more information is needed
- Are the returns to scale of the following production functions increasing, decreasing, or constant? a) Q = KL/4 b) Q = K + L c) Q = Min(K/6, L/3)
- Consider the following production function q=2K^2+L^2. Does this function have returns to scale? If so, which type? Show proof.
- Which of the following production functions exhibit(s) constant returns to scale? I. Q = K + L II. Q = 2K + L III. Q = K0.810.2 a. I and II b. II and III c. I, II, and III d. III only
- Provide a graph and an explanation to show that the production function Q = L0.5K0.5 has a diminishing marginal product of labor but has constant returns to scale.
- How can you determine the returns to scale by just noticing a production function?
- How can we determine the returns to scale by seeing a production function?
- Check if the following production function is constant, decreasing, or increasing return to scale: a. q = K^1/2 L^3/4 b. q = K^1/2 L^4/6
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS). A. q = 10L^{0.6}K^{0.5} B. q = L + K C. q = L^{0.6} + K^{0.5}
- Consider the following production functions: 1. Q=9L+3K 2. Q=10 K0.6L0.4 3. Q=10 min (K, 2L) Which of these production functions exhibits constant returns to scale?s: 1. Q = 9L + 3K 2. Q = 10 K0.6L0.4 3. Q = 10 min (K, 2L) Which of these production functi
- Consider the production function f(x_1, x_2) = x_1^{1/2} x_2^{3/4} . Show that it presents increasing returns to scale.
- Find the returns to scale for the following production function where q denotes output, and x_1, x_2, and x_3 are inputs. q = (2x_1 + x_2)^{2/3} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- Suppose you have a production function equal to Q= 10(0.7K2+0.3L2)0.5. Does this function exhibit a. increasing, b. decreasing, or c. constant returns to scale? Explain.
- State whether the following production functions exhibits constant, increasing or decreasing returns to scale. Assume in all cases {bar}() A is greater than 0. 1) Y = 1/2*K + L 2) Y = L^(3/2) + K^(5/
- Determine which of the following production functions exhibit constant returns to scale (CRS). Hint: Using scale up to double the inputs used, does the output double, less than double, or more than do
- Do the following production functions exhibit decreasing, constant, or increasing returns to scale? You must show calculations to justify your answers (a) Q = 0.5KL (b) Q = 2K + 3L (c) Q = L + L1/2
- Let a production function exist such that Q = K^{0.35}L^{0.75}. A. Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain. B. What is the effect on Q of a 10% increase in labor hours, keeping K constant? C. Wha
- If the production function in a country is Y = the square root of K, the investment rate equals 0.25, and the depreciation rate is 0.05, then the steady-state level of output is equal to A. 5 units. B. 10 units. C. 25 units. D. 15 units.
- Consider the following production function F(K, L) = { KL } / {K + L } (a) Does it satisfy the Constant Returns to Scale Assumption? Explain. (b) Are marginal products diminishing? Explain. (If you can't find marginal products mathematically, you can com
- The production function for outdoor benches is given by: q = (K0.5 + L0.5)2, where the variables are as usual. Does this production function exhibit constant returns to scale? Provide a general algeb
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS)?
- Consider the production function: Q = K^(1/3) L^(2/3) where Q is quantity of output, K is capital, and L is labor. Does this function exhibit increasing, diminishing, or constant returns to scale?
- Find the returns to scale for the following production function where q denotes output, and x_1 and x_2 are inputs. q = ( min { x_1, 2x_2 } )^{1/4} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- Consider a price taking firm which has a Constant Returns to Scale production function. Explain with appropriate diagram of all of the three cases in the following statement: a. The firm either produc
- Consider the following production function: Q = L^AK^0.45. If this production technology exhibits constant returns to scale, what must be the value of A?
- Determine whether the following production function exhibits constant increasing or decreasing returns to scale in capital and labor. A). Y = AK^\frac{3}{4} L^\frac{3}{4}
- Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Q = L + L/K
- a. Derive the LR eqm or steady-state (SS) values of Y/NA and K/NA if the production function is Y=K6/7 (AN)1/7. Does this production function exhibit the characteristics it should? Explain and show these traits mathematically. Graph the LR eqm or SS in th
- Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? a. q = L + K, a linear production function, b. q = L^{\alpha}K^{\beta}, a general Cobb-Douglas production function.
- Suppose firms have the following production function This production function exhibits a. Increasing returns to scale b. Decreasing returns to scale. c. Constant returns to scale. d. The returns to sc
- If the production function for a certain good exhibits constant returns to scale, does this mean that the law of diminishing marginal returns does not apply?
- If the equation Y = F(K,L) represents a constant returns to scale production function, then for any positive constant c the following must also hold: Select one: a. Y = F(cK,cL). b. cY = cF(K,L). c. c
- Consider the Production Function, Y = 25K1/3L2/3 (a) Calculate the marginal product of labor and capital (b) Does this production function exhibit constant/increasing/decreasing returns to scale? (
- With capital K and labor L input, there are five production functions in the following: I. Q = L+K II. Q = Square root L*K III. Q = L*K IV. Q = Cube root L*K V. Q = Lsquare +Ksquare a. Which function(s) exhibit the constant returns to scale? b. Which
- A production function may exhibit _____. a. constant returns to scale and diminishing marginal productivities. b. increasing returns to scale and diminishing marginal productivities. c. decreasing returns to scale and diminishing marginal productivities.
- With capital K and labor L input, there are five production functions in the following: I. Q = L + K II. Q = \sqrt{L \cdot K} III. Q = L \cdot K IV. Q = \sqrt[3]{L \cdot K} V. Q = L^2 + K^2 a. Which function(s) exhibit the constant returns to scale? b. Wh
- 2. determine the returns to scale for the following production functions: (a) Q=(L+K)2 (b) Q=(L(1/2)+K(1/2))2 3. A firm's production function is given by q = 5L2/3 K1/3 (a) Calculate APL and MPL. D
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- Country A and B both have the production function Y = K^\frac{1}{3} * L^\frac{2}{3}. Which of the following is the per-worker production function for both countries? a) y = k^\frac{1}{3}. b) y = k^\fr
- Draw a graph and provide an explanation to show that the production function Q = L0.5K0.5 has a diminishing marginal product of labor but has constant returns to scale.
- Determine whether the production function exhibits increasing, constant or decreasing returns to scale. Q = L^(0.5) K^(0.5)
- What is the returns to scale for each of the following production functions? a. y=K^1/2L^1/3 b. 3K^0.25 L c. y=50(K^1/2}+L^1/2) d. y=1.40(x^0.6+y^0.6)^2
- Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answers. A. The production function Q = M^{0.5}K^{0.5}L^{0.5}, where M is materials, K is capital, and L is labor. B. q = L + 0.5K C. q = 0.5LK^{0.25} D.
- If a production process displays diminishing returns for all inputs, then: a) It cannot display constant returns to scale. b) It cannot display increasing returns to scale. c) It must display decreasing returns to scale. d) All of the above. e) None of th
- For each of the following production functions, are there Increasing returns to scale, constant returns to scale, decreasing returns to scale, or does the answer depend on output level: - A. B. C. D.
- Which term describes this production function's returns to scale?
- For the following production function, please do the following: Y = aK + bL; a, b > 0 a. Find whether they have increasing, constant, or decreasing returns to scale b. Draw the isoquant map for two or
- If the production function is given by Y = K^1/4 L^3/4 and K = 81 and L = 2.52, total output equals about: a. Y = 1 b. Y =0.3 c. Y =22.1 d. Y =6.0 e. Y =82.4 Consider the economies. If each country ha
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = Min(2K, 2L)
Explore our homework questions and answers library
Browse
by subject