Given the function f(x,y) = x²+y²+2xy-8x-8y defined on the set D = {(x, y) = R²: (x − 2)² ≤ y ≤ x} - a. Can it be concluded directly (by examining f and D) whether f reaches a maximum and minimum in D? b. Derive the conditions of the Kuhn-Tucker theorem for the problema and find its solution: max f(x, y) = x² + y² + 2xy - 8x − 8y s.a. (x-2)² ≤ y y≤ x -

Given the function f(x,y) = x²+y²+2xy-8x-8y defined on the set D = {(x, y) = R²: (x − 2)² ≤ y ≤ x} - a. Can it be concluded directly (by examining f and D) whether f reaches a maximum and minimum in D? b. Derive the conditions of the Kuhn-Tucker theorem for the problema and find its solution: max f(x, y) = x² + y² + 2xy - 8x − 8y s.a. (x-2)² ≤ y y≤ x -

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

See similar textbooks

Similar questions

Define the conditions for a weakly quasi-concave Cobb-Douglas Function
2- Answer the following questions: a) Show that Young's Theorem holds for the following function: f(x, y) = 9ye²xy. | b) Let z(x, y, w) = x² + wy +w², where w (r, s) = r² + s²₂ x (r,s) = r² — s² and y (r, s) = r. s. Find the partial derivative 6 =? 6s c) The foreign demand for our exports X depends on the foreign income X and our price level P: 1 X = Y + P-². Find the partial elasticity of foreign demand for our exports with respect to que price level. d) If production function is Q₁ = A(t) K³L, where A(t) is an increasing function of t, and K₁= Ko + at, and L. Lo + bt. Find the rate of change of output with respect to time? = www wwwww.w intim um momw
Is the function v(x1,x2)=x21x32 a monotonic transformation of u(x1,x2) ? Select one: a. No b. Yes
f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.
The Augsburg math club paid $200 for fancy souvenir water bottles that they are going to sell next year for $6 each at the Taste of Augsburg during Homecoming Weekend. Define two variables that relate quantities in this story. Which one is the input of this function and which one is the output? Write an equation for your function, and briefly explain why your function is valid.
Write the following system of equations in the matrix form AX = B;where. Quesiton is in the image
Given the function f(x) = ln (x+1), x>0 In applying mathematical methods to economics/business problems, we use a broad menu of functions for the purpose of accurately specifying the properties of the economic variables in question. Find an example that you can use the above function to describe certain economic or business activity.
Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y = 44t + 0.5t2 − t3, 0 ≤ t ≤ 6. (a) Find the critical values of this function. (Assume −∞ < t < ∞. Enter your answers as a comma-separated list.) t = (b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.) t = (c) For which values of t, for 0 ≤ t ≤ 6, is y increasing? (Enter your answer using interval notation.)
In a certain store, cashiers can serve 45 customers per hour on average. If a customers arrive at the store in a given hour, then the average number of customers C waiting in line can be modeled by the function x² C(x) = 2025 - 45x where x < 45. Answer the following questions with a graphing calculator. Round your answers to integers. 1) If 40 customers arrived in the store in the past hour, there are approximately 7 2) If there are 2 customers waiting in line, approximately customers waiting in line. customers arrived in the past hour.
Could I have help finding these given the two equations and parameter provided above
C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?
What are the three Gauss–Markov conditions? Explain.