Q: What is the elasticity of substitution, o, of the CES production function below? q = (alº + bk°) P…
A: Elasticity is defined as the degree or measure of the change in a variable due to fluctuation in…
Q: 1. Given the production function Q = f(L,K) = KL2 – L3 , where Q is output and L and K are the labor…
A: "Since you have asked multiple question ,we will solve the first question for you.If you want any…
Q: Suppose MPL = 0.5 ∗ (q/L) and MPK = 0.5 ∗ (q/K). In the long run, the firm will hire equal amounts…
A: MPL and MPK are the marginal productivites of labor and capital. Each firm produces the good with…
Q: Consider a firm who owns capital K and has the following production technology Y = zF(K, N)= 2K³N³,…
A: A production function is a mathematical equation that expresses the relationship between the number…
Q: )1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use thi
A: a. Q = (kp + lp)1/p MPK =dq/dk=1/p*p*kp-1*[(kp +lp)1/p-1 ]=[(kp +lp)1-p/p]/k1-p =q/k1-p MPL…
Q: Assuming labor is the only variable factor and paid at a constant wage rate ? show that the average…
A: The productivity metrics (TP, AP, and MP) and the cost measures have some significant correlations.…
Q: In a certain country, output is produced using only labor and land. The production function is…
A: Given information Y = AXα L1-αSubstitute x = 100 and L = 30 Y = A100α 301-α
Q: A firm has the production function Q = 20K02 L0.8, where Q measures output, K represents machine…
A: Q = 20K0.2 L0.8 MPL = ∂Q∂L
Q: Suppose a firm has a production function with two inputs, capital (K) and labor (L). The production…
A: DISCLAIMER “Since you have asked multiple question, we will solve the first 3 subparts for you. If…
Q: For questions 11-14: Suppose a firm's production function is given byes q = 8/Ew + Ep, where Ew and…
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: What is the marginal product of capital (MPK) for the following production function Q = min {L, K} ?…
A: Production function: Q = min {L , K} The above production function depicts that input Labor (L) and…
Q: a)What is the initial population of Cobra Island? b)Let the wage of labor is 0.4, and the rental…
A: (Note: Since there are multiple questions, the first three have been solved). The Solow model…
Q: Consider the C -Douglas production function q a. Find the RTS and show that it is decreasing in l.…
A: here we can determine the given equations as follow
Q: If more and more labor is employed while keeping all other inputs constant, the marginal physical…
A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…
Q: The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L =…
A: Hey, Thank you for the question. According to our policy we can only answer up to 3 sub parts per…
Q: The following are correct statements about the Marginal Productivity of Labor (MPL), EXCEPT:…
A: The marginal product of labour in economics is the change in output that results from employing an…
Q: Consider the production function of widget: Q= 23K"^L°.8, where Q is units of output per month, K is…
A: Given; Production Function; Q=23K0.4L0.8 where; Q= Output per unit K= Hours of capital L= Hours of…
Q: Suppose there are two primary factors of production, labour (L) and capital (K), and there are…
A: Given Production function Y=cKL ........ (1) where c is constant K denotes capital and L denotes…
Q: In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population…
A: Note: Since we can only answer up to three subparts, we'll answer the first three subparts. Please…
Q: Some economists believe that the US. economy as a whole can be modeled with the following production…
A: As we know that Cobb-Douglas production function models represents the relationship among production…
Q: . Consider the following information of a hypothetical fırm: Q = 100K0.6 L0.8; w = 1; r = 3 %3D A.…
A: Given Production function: Q=100K0.6L0.8 .... (1) wage rate w=1 and rent r=3
Q: Y = AK" L¹". Also assume that the supplies of capital and labor are fixed at K and I, respectively.…
A: Cobb-Douglas: The Cobb-Douglas creation capability is a specific utilitarian type of creative…
Q: Given the production function Y=(lp +kp)1/p, what is the technical rate of substitution, the…
A: A production function is a mathematical and occasionally graphical method of calculating production…
Q: A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is…
A: Returns to scale basically the returns obtained in a long period of time when the production scales…
Q: In 2008, the country of Cobra Island has an initial level of capital set at 10 units. The population…
A: Given, production function, Y=10*L1/2K1/2 L is Labour K is Capital Capital is given as 10 units…
Q: Consider a Cobb-Douglas production function: f(l, k) = Alα k1−α , where A is the total factor of…
A: Since you have provided multiple parts and multiple subpart question, we will solve the first three…
Q: Consider the following production function: q= 100L0.8K0.4 Currently the wage rate (w) is $15.00 and…
A: Cost is minimized at condition,
Q: Consider the production function F(K,L) = In(K*L). What is the marginal product of capital equal to…
A: Given Production function: F(K,L)=lnKL ... (1) We have to calculate MP of capital at…
Q: Suppose the production function for widgets is given by q=kl-0.8k².0.212 where q represents the…
A: The production function shows all the combinations of labor and capital inputs that can be used to…
Q: Y=$10 trillion, K=$10 trillion, L=100 million workers Cobb-Douglas Production Function What is…
A: Production function shows the relationship between the physical output and physical inputs.…
Q: Suppose that the output Q (in units) of a certain company is Q = 75K¹/32/3, where K is the capital…
A: Given information: Q=75K13L23
Q: F (L, K) = L0.2K0.7， The wage rate (price per unit of labour) is w = 2 and the capital rental rate…
A: Answer in step 2.
Q: Given the Production function for Mwaba & Mutale Enterprises as follows: Q = f (k,l) = 300k 2l2 - k…
A: Introduction Production is said to be the transformation of input into output. Total product is the…
Q: inction: Consider the 'Cobb-Douglas' production function: f(k;, n4) = ki'n}-a where a is an…
A: The marginal products are calculated by differentiating total output with respect to the inputs viz.…
Q: Consider an economy characterized by the production function Y = ĀK2 L"2 where the productivity…
A: PRODUCTION FUNCTION = Y = AK1/2L1/2
Q: Suppose there is a firm who hires workers as part of their production. The firm makes use of two…
A:
Q: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = WK" L1-r…
A:
Q: With a Cobb-Douglas production function of Y = K$L5, What are the marginal product of capital and…
A: A production function illustrates the relationship between the inputs used and output produced in a…
Q: Suppose the Cobb-Douglas production function is given as: , where b0 = level of technology, b1 =…
A: “Since you have asked multiple subparts, we will solve the first three parts for you. If you want…
Q: Given the production function y=(l^p+K^p)^1/p, what is the technical rate of substitution and the…
A:
Q: A profit maximizing firm produces output using capital, K, and labour, L, in the following…
A: Profit is maximized when the marginal rate of technical substitution is equal to the ratio of prices…
Q: The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L =…
A: (Note: Since, the question has multiple parts, the first three have been solved. Please resubmit the…
Q: 1) Suppose a firm uses capital, K, and labor, L, to produce output. Verify whether the following…
A: Note; Since we can only answer up to three subparts, we'll answer first three please repost the…
Q: Consider the following production function: q = 100L0.8K0.4 Currently the wage rate (w) is $4.00 and…
A: Cost is minimized at the optimal level of production.
Q: Given the production function y=(l^p + k ^1/p )^1/p , what is the technical of substitution, the…
A: Technical of substitution. The marginal pace of technical substitution (MRTS) is a monetary theory…
Q: The Long-run production function is given by; Y = 180 L0.8 K1.8Where, Y = Output (mt/day), L =…
A: (a) The marginal product of a factor shows the amount by which output changes due to employment of…
Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where krepresents capital and l represents labora. Show that MPk = (q/k)1 and MPl = (q/l)1 .b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ).c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input.Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price oflabor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
- Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where k represents capital and l represents labora. a. Show that MPk = (q/k)1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ). c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input. Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)Given the production function y=(l^p + k ^1/p )^1/p , what is the technical of substitution, the elasticity of substitution, and the returns to scale when p = 0.5?1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
- (A) Suppose the production function for T-shirts can be represented as q = L0.5 KO.5. Show that the marginal productivity of labor diminishes in the short run. What is the cost minimizing bundles of labor and capital in the long run for T-shirts where w = and r = 10 when q=100 units?From the following production functions 1. Q= a1H + a2L + a3H2 + a4 L2 + a5HL, where ai> 0 2. Q = aH@ Ly, where a, @, y > 0 a. Derive the equation of the relevant isoquant. b. Find out whether the production function is well behaved. c. Examine whether the isoquant is well behaved and therefore represents the behaviour of a rational production. d. Derive equation which describes MRTS of 9ne factor. e. For each equation examine whether the production is homogeneous and if so, what is the degree of homogeneity. Is the equation characterized by IRTS, DRTS or CRTS.2) Consider the production function q = f(L, K) = ALªK®, where A, a, b are positive constants. For what values of A, a, and b are there diminishing marginal returns to labor L? What about diminishing marginal returns to capital? b. For what values of A, a, and b does the production process have diminishing marginal rate of technical а. substitution? с. For what values of A, a, and b are there constant/decreasing/increasing returns to scale?A Firm's Optimization with CES Production Function The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substitution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(Kt, Nt) = [aK{ + (1 − a)N]¹º 0Recommended textbooks for you
Managerial Economics: Applications, Strategies an…EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning
Microeconomics: Principles & PolicyEconomicsISBN:9781337794992Author:William J. Baumol, Alan S. Blinder, John L. SolowPublisher:Cengage Learning
Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
Managerial Economics: Applications, Strategies an…EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage LearningMicroeconomics: Principles & PolicyEconomicsISBN:9781337794992Author:William J. Baumol, Alan S. Blinder, John L. SolowPublisher:Cengage LearningEconomics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning