ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 7
1. Suppose that the output q of a firm depends on the quantities of z1 and z2 that it employs as inputs. Its output level is determined by the production function
2 2 q = 26z1 + 2
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 5
1. Consider the firm with a single factor of production defined implicitly by the relation z = q3 + 4q where z is the variable input and q is output. The firm faces the following
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 4
Qd = kP - ( > 0)
Qs = c(P - T0 )
are the demand and supply curves for a commodity whose price is P. T0 is a sales tax imposed by the government on sales of this commodity. (a) Com
ECON 331 Final Exam
Saturday, April 12, 1997 K. Wainwright Instructions. - Put you name on the EXAM and the Booklets you use for your answers. - The Exam Sheet must also be handed in as proof you wrote the test. - Time allowed is 2.5 HOURS. Total marks =
1
Selected answers to practice final 1
Spring 1998 (A) Question 1. The profit function: = pq - wL - rK = p(60K + 34L - 4KL - 6K 2 - 3L2 ) - wL - rK The FOC's give: 34 - 4K - 6L - w = 0 p r 60 - 4L - 12K - p = 0
which can be solved for K and L. i.e. by Cra
ECON 331 Final Exam Spring 1998 (a)
Name:
Instructions:The exam is worth 60 marks. All questions are equally weighted. You are to do all questions.
Answer all questions in the exam booklets provided.
Time allowed is 3 hours. You must hand in the exam
with
ECON 331 Tutorial Questions #3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Find y' if y = (x 3 - 10x + 2)(x 2 + 7x + 1). 2) Find y' if y = 2x + 3 . 7 - 5x x 2 + 1. . 2x 3 - 1 2x + 5 at the point (4
Partial Solutions to Practice Final #2 1. Minimize z = 3x2 xy + 2y 2 4x 7y + 12 subject to the inequality constraint x + y 15. Is the constraint binding or non-binding?ANSWER L = 3x2 xy + 2y 2 4x 7y + 12 + (x + y 15) kuhn-tucker Lx Ly L = 6x y 4 + 0 x0 =
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Two Variable Optimization Using Calculus For Maximization Problems
One Variable Case
If we have the following function y = 10x - x2 we have an example of a dome shaped function. To find the maximum of the dome, we simply need to find the point where the s
Multivariable Calculus Partial Derivatives
Single variable calculus is really just a "special case" of multivariable calculus. For the function y = f (x), we assumed that y was the endogenous variable, x was the exogenous variable and everything else was
ECON 331
Tutorial Homework for Week One
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) 3 -1 4 -1 Perform the indicated operations and simplify your answer: 4 2 + 2 0 5 6 -8 -4 3 2) Perform the indicat
ECON 331
Study Questions for Chapter 12: Lagrange Multiplier Method
Kevin Wainwright
SHORT ANSWER. Show all your work. In each case, check 2nd order conditions 1) Use the method of Lagrange multipliers to find the critical points of f(x, y, z) = 2x + 4y -
ECON 331 Tutorial Questions
Topic: Implicit Differentiation and Chain Rule
Note: Where necessary, rewrite funtions into the form: F(x,y,z)=0 and use implicit function Theoem. For Multiple choice, SHOW your work MULTIPLE CHOICE. Choose the one alternative
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 10 ANSWER KEY
1. A new cellphone company Yap.com is setting up in Burnaby and it has to plan its capacity. The peak period demand is given by p1 = 200 0:25q1 and the o-peak is given
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 10
1. A new cellphone company Yap.com is setting up in Burnaby and it has to plan its capacity. The peak period demand is given by p1 = 200 0:25q1 and the o-peak is given by p2 = 19
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 9 Answer Key
1. Given the utility maximization problem Max U = xy subject to B = px x + py y (a) Derive an expression for the Slutsky equation for x and y when px changes. Identify
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 9
1. Given the utility maximization problem Max U = xy subject to B = px x + py y (a) Derive an expression for the Slutsky equation for x and y when px changes. Identify the income
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment 8
Skip has the following utility function: U(x, y) = x(y + 1), where x and y are quantities of two consumption goods whose prices are px and py respectively. Skip has a budget of B.
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homwork Assignment 3
From homework assignment 2 we had the following demand functions:
d q1 = 20 2p1 + p2 d q2 = 25 + p1 3p2
Use Cramers Rule to nd the inverse demand functions Pi = f (qi , qj ) i = 1,
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment #2
[1] In the interest of prudent diversication, an investor wishes to have his $100 of wealth invested as $50 in the Canadian economy, $30 in the U.S. economy, and $20 in the Engli
ECONOMICS 331 Mathematical Economics Kevin Wainwright
Homework Assignment #1
[1] Two markets for two commodities interact with each other in the sense that the demand for each product depends not only on its own price, but also on the prices of other prod
Envelope Theorem
Kevin Wainwright Mar 22, 2004
1
Maximum Value Functions
A maximum (or minimum) value function is an objective function where the choice variables have been assigned their optimal values. These optimal values of the choice variables are, i
ECON 331
Tutorial Questions #2 Problem 1 Find AB = C If A= 5 1 0 2 1 1 and 4 3 B= 1 1 0 2 B= 1 0 1 0
Problem 2 Find both C = AB and D = BA if 1 2 A= 2 1
and
Problem 3 Find the determinant by LAPLACE Expansion of 1 2 3 A = 0 1 1 1 2 3
1 Problem 4 Find the
ECON 331 Tutorial Questions: 2 Variable optimization Make Sure to check second order conditions for all solutions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopolist produces two products,
ECON 331 Tutorial Questions: Onve Variable Optimization (Chapter 9) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) The profit equation for a taco stand is given by P(x) = -0.4x 2 + 100x - 100, where x