CDAE 266 - Class 10
Sept. 27
Last class:
Result of Quiz 2
Project 1
2. Review of economic and business concepts
Today:
2. Review of economic and business concepts
Next class:
2. Review of economic and business concepts
3. Linear programming
Important dates:
Project 1: due Tuesday, Oct. 2
Problem set 2: due Tuesday, Oct. 9
Problem set 2
Problems 2.1., 2.2., 2.4., 2.5. and 2.8. from the reading “Basic
Economic Relations”
-- Due Tuesday, Oct. 9
-- Please use graphical paper to draw graphs
-- Please staple all pages together before you turn them in
-- Scores on problem sets that do not meet the requirements will be discounted
Questions for Problem 2.4.:
A. Construct a table showing Christensen's marginal sales per day in each state.
B. If administrative duties limit Christensen to only 10 selling days per month,
how should she spend them (i.e., how many days in each state)?
C. Calculate Christensen's maximum monthly commission income.
One more application of TVM
(Take-home exercise, Sept. 27)
Mr. Zhang in Beijing plans to immigrate to Canada and start a
business in Montreal and the Canadian government has the
following two options of “investment” requirement:
A. A one-time and non-refundable payment of $120,000 to the
Canadian government.
B. A payment of $450,000 to the Canadian government and the
payment (i.e., $450,000) will be returned to him in 4 years from the
date of payment.
(1)
(2)
(3)
(4)
How do we help Mr. Zhang compare the two options?
If the annual interest rate is 12%, what is the difference in PV?
If the annual interest rate is 6%, what is the difference in PV?
At what interest rate, the two options are the same in PV?
2. Review of Economics Concepts
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
Overview of an economy
Ten principles of economics
Theory of the firm
Time value of money
Marginal analysis
Break-even analysis
2.5. Marginal analysis
2.5.1.
2.5.2.
2.5.3.
2.5.4.
2.5.5.
2.5.6.
2.5.7.
Basic concepts
Major steps of using quantitative methods
Methods of expressing economic relations
Total, average and marginal relations
How to derive derivatives?
Profit maximization
Average cost minimization
2.5.5. How to derive derivatives?
The first-order derivative of a function
(curve) is the slope of the curve.
(1) Constant-function rule
(2) Power-function rule
(3) Sum-difference rule
(4) Examples
2.5.6. Profit maximization
(1) With a profit function (relation between profit
and output quantity):
(a) Profit function:
  10,000  400Q  2Q
2
(b) What is the profit-maximizing Q?
-- A graphical analysis
-- A mathematical analysis
d
M 
 0  400  4Q
dQ
Set M = 0 ==> Q* = 100
(c) Maximum profit = 10,000
2.5.6. Profit maximization
(2) With TR and TC functions:
--  is at the maximum when M = 0
-- Relations among M, MR and MC:
 = TR - TC
d dTR dTC


dQ dQ
dQ
M = MR - MC
M = 0 when MR = MC
-- Graphical analysis (page 5 of the handout)
 is at the maximum level when
MR=MC
-- An example:
2.5.6. Profit maximization
(3) With TC and demand functions:
-- Demand function: Relation between Q and P
Example: Q = 2000 – 0.26667 P
-- Derive TR function from a demand function
Example: Demand function  P = 7500 -3.75Q
TR = P*Q = (7500 – 3.75Q) Q
= 7500Q - 3.75Q2
-- Derive the MR and MC
dTR
MR 
dQ
dTC
MC 
dQ
-- Set MR = MC and solve for Q*
2.5.6. Profit maximization
(3) With TC and demand functions:
-- An example from the handout:
Demand: Q = 2000 – 0.26667 P
Total cost: TC = 612500 + 1500Q + 1.25Q2
-- Demand function  P = 7500 – 3.75Q
-- TR = P*Q = (7500 – 3.75Q) Q = 7500Q - 3.75Q2
-- TR  MR = 7500 - 7.5Q
-- TC  MC = 1500 + 2.5Q
-- Set MR = MC  7500 - 7.5Q = 1500 + 2.5Q
-- Q* = 600
-- P = ? TC = ? TR = ?
=?
2.5.6. Profit maximization
(4) Summary of procedures
(a) If we have the total profit function:
Step 1: Take the derivative of the total profit function 
marginal profit function
Step 2: Set the marginal profit function to equal to zero and
solve for Q*
Step 3: Substitute Q* back into the total profit function and
calculate the maximum profit
(b) If we have the TR and TC functions:
Step 1: Take the derivative of the TR function  MR
Step 2: Take the derivative of the TC function  MC
Step 3: Set MR=MC and solve for Q*
Step 4: Substitute Q* back into the TR and TC functions to
calculate the TR and TC and their difference is the
maximum total profit
2.5.6. Profit maximization
(4) Summary of procedures
(c) If we have the demand and TC functions
Step 1: Demand function  P = …
Step 2: TR = P * Q = (
)*Q
Then follow the steps under (b) on the previous page
Class Exercise 4
(Thursday, Sept. 27)
1. Suppose a firm has the following total
revenue and total cost functions:
TR = 20 Q
TC = 1000 + 2Q + 0.2Q2
How many units should the firm produce in
order to maximize its profit?
2. If the demand function is Q = 20 – 0.5P, what
are the TR and MR functions?