) Say you were interested in maximizing U = U(x,y) with the usual budget constraint,M = Px*x+Py*Y.Explain the comparative statics process for determiningDo not perform the finalÔMcalculation, only get as far as the Cramer's rule expression forÔM

Given, Utility function : U=U(x, y)Budget Constraint : M=Px*x+Py*y

Answered: Say you were interested in maximizing U…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Which of the following conditions should hold for an interior optimum? Px MRSXY and PxX + PyY < I Py MUx and MUy should be maximized and Px X + PyY = I Px MRSXY and PxX + PyY = 1 Py MRSXY should be maximized and PxX + PyY = I
.A company can sell its only product and in a perfectly competitive market at a price of 15. To produce it, it must purchase two production inputs: labor (x1) and machinery (x2). Initially, the company only has 1 machine and it is not possible to change this in the short term. Inputs are purchased in competitive markets with respective prices (w1, w2) = (5,10). The production function is as follows: 3 2/3 1/3 f(x,x2) a) Present the problem of maximization of the company. b) Find the first order condition that must be solved to find the optimal level of supplies. c) Find the optimal input level x1 that the company must contract in the above problem to maximize your profits.
The demand and supply of pizza is defined by the following equations: Qd = D(P, Y ) = 1 + Y − 2P Qs = D(P, PM) = 2 P/PM where, Qd is quantity demand, P is the price of each pizza sold, Y is the average income of consumers, Qs is the quantity supplied, and Pm is the price of inputs used in the production of pizza. (a) List the endogenous and exogenous variables of this model (b) Find the equilibrium price Pe and quantity Qe of pizza as a function of the exogenous variables. (c) Use a simple demand and supply diagram to show what happens to the equilibrium price and quantity when there is an increase in one of the exogenous variables.
Suppose you have the following indirect utility function: V(Pa, Py, I) = In PxPy What are marshallian demands for x and y? I (a) (9x9y) = (22) (b) (9,9y) = (In, In 2) (c) (9, 9y) = (exp(2p/py), exp(2ppy)) I (d) (9x, gy) = (2pr+py' px+2py) What is the expenditure function for the associated expenditure minimization problem? (a) E(pa, Py, U) = (P + Py) ln(U) (b) E(pa, Py, U) = √exp(U)Papy (c) E(pa, Py, U)= (p²+p²) In(U) (d) E(pa, Py, U) = exp(U)²papy What are the individual's Hicksian demands for goods x and y? (a) (h₂, hy) = ((BU)¹/², (PU) ¹/²) (b) (ha, hy) = (RU, DU) (c) (ha, hy) = ((2 exp(U))¹/², (exp(U))¹/²) -1/2 (d) (hx, hy) = ((P₂PzU)−¹/², (P₂PzU)-¹/2) Are x and y complements or substitutes?
Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe 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?
Production. Assume a production with two variable inputs (L, K). Show graphically the following and explain: (a) fixed-proportions production function (b) inputs are perfect substitutes
Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.
The time path of resources is described by X(t) = X(0)e*". If you graphed In X(t) on the y-axis, and had time (t) on the x-axis, then what would be the intercept of the line you drew? In X(0) There isn't enough information to tell gx

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Say you were interested in maximizing U = U(x,y) with the usual budget constraint, M = Px*x+Py*Y. Explain the comparative statics process for determining Do not perform the final ÔM calculation, only get as far as the Cramer's rule expression for ÔM

Say you were interested in maximizing U = U(x,y) with the usual budget constraint, M = Pxx+PyY. Explain the comparative statics process for determining Do not perform the final ÔM calculation, only get as far as the Cramer's rule expression for ÔM