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CDAE 266 - Class 11 Oct. 2 Last class: 2. Review of economic and business concepts Today:

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CDAE 266 - Class 11

Oct. 2

Last class:

2. Review of economic and business concepts

Today:

2. Review of economic and business concepts

3. Linear programming and applications

Next class:

3. Linear programming

Quiz 3 (sections 2.5 and 2.6)

Important dates:

Project 1: due today

Problem set 2: due Tuesday, Oct. 9

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.:

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.

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.

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.

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. Overview of an economy

2.2. Ten principles of economics

2.3. Theory of the firm

2.4. Time value of money

2.5. Marginal analysis

2.6. Break-even analysis

2.5. Marginal analysis

2.5.1. Basic concepts

2.5.2. Major steps of using quantitative methods

2.5.3. Methods of expressing economic relations

2.5.4. Total, average and marginal relations

2.5.5. How to derive derivatives?

2.5.6. Profit maximization

2.5.7. Average cost minimization

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

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?

2.5.7. Average cost minimization

(1) Relation between AC and MC:

when MC < AC, AC is falling

when MC > AC, AC is increasing

when MC = AC, AC reaches the minimum level

(2) How to derive Q that minimizes AC?

Set MC = AC and solve for Q

2.5.7. Average cost minimization

(3) An example:

TC = 612500 + 1500Q + 1.25Q2

MC = 1500 + 2.5Q

AC = TC/Q = 612500/Q + 1500 + 1.25Q

Set MC = AC

Q2 = 490,000

Q = 700 or -700

When Q = 700, AC is at the minimum level

2.6. Break-even analysis

2.6.1. What is a break-even?

TC = TR or = 0

2.6.2. A graphical analysis

-- Linear functions

-- Nonlinear functions

2.6.3. How to derive the beak-even point or

points?

Set TC = TR or = 0 and solve for Q.

TR

TC

B

Costs ($)

A

FC

Break-even quantity

Quantity

TC

TR

Costs ($)

Break-even quantity 1

Break-even quantity 2

Quantity

2.6. Break-even analysis

2.6.4. An example

TC = 612500 + 1500Q + 1.25Q2

TR = 7500Q - 3.75Q2

612500 + 1500Q + 1.25Q2 = 7500Q - 3.75Q2

5Q2 - 6000Q + 612500 = 0

Review the formula for ax2 + bx + c = 0

x = ?

e.g., x2 + 2x - 3 = 0, x = ?

Q = 1087.3 or Q = 112.6

1.Suppose a company has the following total cost (TC) function:

TC = 200 + 2Q + 0.5 Q2

(a) What are the average cost (AC) and marginal cost (MC) functions?

(b) If the company wants to know the Q that will yield the lowest average cost, how will you solve the problem mathematically (list the steps and you do not need to solve the quadratic equation)

2.Suppose a company has the following total revenue (TR) and total cost (TC) functions:

TR = 20 Q

TC = 300 + 5Q

How many units should the firm produce to have a break-even?

3. Linear programming & applications

3.1. What is linear programming (LP)?

3.2. How to develop a LP model?

3.3. How to solve a LP model graphically?

3.4. How to solve a LP model in Excel?

3.5. How to do sensitivity analysis?

3.6. What are some special cases of LP?