A firm is able to adjust both L and K and has a production function q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is r and the cost per unit of labor is w. The (conditional) demand for capital (also known as the optimal level of capital) is given by:
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- Sam Malone is considering renovating the bar stools at Cheers.The production function for new bar stools is given byq = 0.1k 0.2l0.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stoollathes used during the week, and l represents the number ofworker hours employed during the period. Sam would like toprovide 10 new bar stools, and he has allocated a budget of$10,000 for the project.a. Sam reasons that because bar stool lathes and skilled barstool workers both cost the same amount ($50 per hour),he might as well hire these two inputs in equal amounts.If Sam proceeds in this way, how much of each input willhe hire and how much will the renovation project cost?b. Norm (who knows something about bar stools) arguesthat once again Sam has forgotten his microeconomics.He asserts that Sam should choose quantities of inputs sothat their marginal (not average) productivities are equal.If Sam opts for this plan instead, how much of…Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?BereketIf the production function of a firm is given by Q=K^2L^3 and the input prices are r=Birr 8 per unit and w= Birr 2 per unit, find the levels of labor and capital that maximize the level of output bfor a total outlay of birr 240.
- The Constant Elasticity of Substitution (CES) production function is a flexible way to de- scribe 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 substi- tution 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(KN)=[αK² +(1−a]N₁°]¹/º, 0The Constant Elasticity of Substitution (CES) production function is a flexible way to de- scribe 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 substi- tution 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(K₁, N₁) = [aK? + (1 - a) No] 1, 0A manufacturer named Kjell is facing the following product function.1 x = f(N, K) = 100Nº.8K0,2 The price for labor is NOK 500 per unit. The price for capital is NOK 125 per unit. a) Does the product function provide constant, increasing, or decreasing scale benefits? b) Kjell wants to produce 400 cakes at the lowest possible cost. How much labor and does he need capital? What will be the cost? c) The bank is not impressed by Kjell's production technology. He therefore receives a loan of only NOK 1,875. How many cakes can Kjell produce a maximum of NOK 1,875. d) Make a factor diagram (N, K). Note Kjell's adaptation from problem b) and c). Draw the isocost lines and the substituent template. e) A short-term strike leads to the price of labor rising to NOK 750. Kjell still has only NOK 1,875. How will Kjell change his adaptation from c)?How many cakes does he produce now? f) Kjell eventually starts making money, and wants to expand production to 650 cakes. What will be Kjell's new…Consider the production function Q = (0.5K1/3 + 0.5L1/3)3 with a corresponding MRTS = K2/3/L2/3. a. Prove that this production function exhibits constant returns to scale. b. Suppose the firms want to minimize the cost of producing 8 units of output. It pays a wage rate W of $40 and capital cost R of $10. How many units of labor and capital should the firm use?Q(K, L) = 4K²L2 Type your answers in all of the blanks and submit The production function of good x is as follow: a. What is the marginal production of capital with 16 labor and 4 capital? Type your answer her b. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 10 labors and 400 units of capital. Slope = Type your answer her (absolute value.) c. If we increase the amount of labor we use in our production process from 10 to 1000 units, how much change in capital is needed for us to stay on the same isoquant? Change in K= Type your answer here (Actual value, negative if decrease and positive if increase) d. Is diminishing return a characteristic of this production function? For labor? (yes/no) Type your answer her ;For Capital (yes/no)? Type your answer hereThe number of souvenir coffee mugs (in hundreds) that Ace Novelty can produce monthly is given by the production function where x denotes the amount of labor utilized (measured in thousands of work-hours per month) and y denotes the expenditure on capital investment (in thousands of dollars per month). Find the marginal productivities if 10,000 work-hours per month are utilized and a capital investment of $5000/month is made. Interpret your results.Please no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.Suppose a firm hires from the competitive labor and capital market to make strawberries. The per unit price of labor is $w and the per unit price of capital is $r. The firm has raised TC amount of seed money and is deciding to allocate it on hiring labor and capital in the least cost way. The production function of strawberries is written as Q = 25LKb which acts as the production target [0A 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 youManagerial Economics: Applications, Strategies an…EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage LearningEconomics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage LearningManagerial Economics: Applications, Strategies an…EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage LearningEconomics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning