Econ 11B - Mathematics for Economists Part II - Exam 2 Grading and Solutions


Five Questions - fifty points total, ten points each question
 Questions, Answers & Grading Key [PDF]

   Step-by-Step Solutions 

Question 2 - For the function 

(a) Take the first order conditions and determine the critical points. 

(b) Apply the Second Derivative Test to determine whether the critical point is a relative maximum, relative minimum, saddle point or inconclusive.  Solution  

Question 3 - A hiker gets utility from teh consumption of three goods: warm cloths (denoted as c), GORP (g), and sunscreen (s). Each of these items costs $1 per unit. The hikers has $100 to spend. 

(a) Write out the hiker's budget constraint. 

(b) The hiker has a utility function given by 
Find the optimal combination of clothes, GORP and sunscreen that will maximize his utility subject to his budget constraint. Assume that 

Question 4 - Find critical points for the function 

        subject to the constraint, 


Question 5 - Envelope Theorem

(a) State the Envelope Theorem, either in words or in mathematical notation. 

(b) BeaverTails Canada Inc. produces beaver tails using capital and labor according to the following production function: 
The firm's costs are .
The firm receives p dollars for each unit it sells. 
Set up the firm's profit function and find the profit maximizing level of capital and labor.

(c) When the firm produces using the profit maximizing level of capital and labor, what will be the effect on its profits if it increases its price marginally - will profits increase or decrease? By how much? Will a change in the price indirectly affect how much capital and labor are used?

Problem 2 - What it looks like: