For maximization, based on sufficient conditions, what must be the sign of all principal minors of order 3?
In order to answer the given question, the concept of Hessian Matrix is used.
Hessian matrix is a squared matrix of second-order partial derivatives that describes the local curvature of the function with many variables.
For maximization, the sufficient condition is that the principal minors of order 3 alternate in sign with the 1×1 minor being negative.
For maximization, based on sufficient conditions, what must be the sign of all principal minors of...
Problem 1. Please note a correction: A matrix is positive definite if all its lead- ing principal minors are positive and negative definite if the principal minor:s alternate in sign, starting with negative. I got confused and wrote the other way in class on Wednesday. It was a mistake Provide formulas/rules for each of the following: State the necessary and sufficient conditions for maximizing a function with more than two variables. State the necessary and sufficient conditions for minimizing a...
Q1: What are the first and second-order conditions for profit maximization for a firm operating under perfect competition? Give an economic interpretation of both conditions.
1. What is the difference conceptually between a choice based on the maximization of a single objective versus a choice based on maximization with two or more objectives? In each case, what role do tradeoffs play in making the choice?
A consumer must maximize utility, U-f(x.y), subject to the constraint that she spends all her income, M on purchasing two goods x, v. The unit prices of the goods, px and py respectively, are market determined and hence exogenous. (i) State the objective function, constraint, and choice variables of this problem (3 marks) (ii) Obtain the Lagrangean for this problem, using λ to represent the Lagrange multiplier. (3 marks) (i) Obtain the first order conditions of this problem in terms...
What conditions must a property satisfy to be considered depreciable? Choose all the correct conditions below. A. It must be something that wears out, decays, gets used up, becomes obsolete, or loses value from natural causes. B. It must be a personal property such as a copyright, patent, or franchise. C. It must have a determinable useful life, and the life must be longer than one year. D. It must not be used in business or held to produce income....
What conditions are necessary for total internal reflection to occur? Choose all that apply. What conditions are necessary for total internal reflection to occur? Choose all that apply. n2 must be less than n1 θ1 must be less than θc n2 must be greater than n1 θ1 must be greater than θc How do you know the conditions for this?
A consumer must maximize utility, U-for.y), subject to the constraint that she spends all her income, M on purchasing two goods x, y. The unit prices of the goods, p, and py respectively, are market determined and hence exogenous (3 marks) (3 marks) rKS rice marks) (i e1 (2 marks) 0.8,0.2 (d) Let the utility function be U -5x ф Solve the maximization problem in this case (that is obtain x*, y*, 8y0.z and unit prices pr - p- 1...
1. Consider the profit maximization problem for the firm. Say the pro- duction function f(k, n) is strictly concave jointly in all arguments and once continuously differentiable (C), where k (resp, n) denotes the input of capital (resp, labor) (a) Assume a maximum exists for the firms profit maximization problem. What are the first order conditions (FOCs) to characterize all optimal solutions for factor demands for capital and labor in the general problem? (b) Say f(k, n) = (ak" +...
A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $37,000 when the child reaches the age of 18? Assume the money earns 8% interest, compounded quarterly. (Round your answer to two decimal places.)
Costs, income and profit maximization Instructions You must calculate with the information provided everything that is in blue and yellow, once the calculations made you must answer the questions below the table. I remind you that the mathematical procedure must be present in the equations, otherwise the exercise is Invalid. Evaluation: Each question has a value of 8 points and making the table has a value of 4 points, you must be aware of putting the numbers in the table...