Problem B: The Production Model Consider the production model that we have seen in class with a production function for final output specified as Y = K1/4L3/4_ %3D Capital and labor available in the economy are, respectively, K = 40 and L = 50. B.1 Write down the profits maximization problem for firms in the production model (you can write profits in units of final output). Derive the first order conditions for the firm's maximization problem and provide the economic interpretation of the first order condition for labor. B.2 Please define the property of “Constant Returns to Scale" as we did in class. Does the production function above exhibit constant returns to scale? Show your computations.

Problem B: The Production Model Consider the production model that we have seen in class with a production function for final output specified as Y = K1/4L3/4_ %3D Capital and labor available in the economy are, respectively, K = 40 and L = 50. B.1 Write down the profits maximization problem for firms in the production model (you can write profits in units of final output). Derive the first order conditions for the firm's maximization problem and provide the economic interpretation of the first order condition for labor. B.2 Please define the property of “Constant Returns to Scale" as we did in class. Does the production function above exhibit constant returns to scale? Show your computations.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Welfare Analysis

Welfare analysis of the society is related to welfare economics. From the economic point of view former welfare economics refers to that subject which uses the techniques of microeconomics to analyse and evaluate the welfare at the economic or aggregate level.

Question

Problem B: The Production Model
Consider the production model that we have seen in class with a production function for final output
specified as
Y = K1/4L3/4
Capital and labor available in the economy are, respectively, K = 40 and L = 50.
B.1 Write down the profits maximization problem for firms in the production model (you can write profits
in units of final output). Derive the first order conditions for the firm's maximization problem and provide
the economic interpretation of the first order condition for labor.
B.2 Please define the property of "Constant Returns to Scale" as we did in class. Does the production
function above exhibit constant returns to scale? Show your computations.
B.3 State the equations that constitute the competitive general equilibrium for the economy in the
production model above. What are the variables that you need to solve for to obtain a solution to the
equilibrium?

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Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier.
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4.
QUESTION THREE: PRODUCER THEORY 1. Suppose the production function for automobiles is given by q = kl - 0.8k² - 0.21² where q represents the annual quantity of bicycles produced, k represents annual capital input, and I represents annual labor input. a) Suppose k=10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many cars are produced at that point? b) Again, assuming k=10, graph the MP curve. At what level of labor input does MP₁ = 0 c) Suppose capital inputs were increased to k-20. How would your answer to parts (a) and (b) change? d) Does the production of automobiles exhibit constant, increasing, or decreasing returns to scale? 2. Supposing that the firm in (1) is a competitive firm and its production function is y = 10 + (x - 1,000)¹/3. The price of the input x is w = 1. (a) Show that the firm's total cost curve is C(y) = 1,000 + (-10)³. (b) Show that the minimum of the marginal cost curve…
Problem 1 - Macroeconomics - please help.
In economics and econometrics, the Cobb-Douglas production function is a particular functional form of ne production function, widely used to represent the technological relationship between the amounts of two r more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK!-a where P is the total production (the monetary value of all goods produced in a year), L is the amount f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P P(L, K) = 6LªK1-a → In K L In b+ a ln K
Answer the Constrained Optimization: Cobb-Douglas Production Function:3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces
Please answer C and D