ECON 220
Week 1
Introductions
•
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Name
Where you’re from
Why are you interested in Economics
Or
Something interesting about yourself.
Administrative things
• Moodle page: Get your coursepaper, tutorial
worksheets and solutions, and lecture slides.
• Textbook: Varian, Intermediate Microeconomics
• Office hours: Tuesdays 11-11:50, Old Eng. Bldg. C41
• Email: a.ali11@lancaster.ac.uk
• My website:
www.lancaster.ac.uk/pg/alia10/econ220.html
My Expectations
• Read the textbook and keep up with the readings
for each week.
• Attend the lectures and take notes.
• Attempt every question on the weekly
worksheets.
• Bring completed work, any questions that you had
to tutorials.
• Participate in tutorials: discussions, group work,
individual work at the board.
What we’ll do in Tutorials
• Discuss answers to some worksheet questions.
• Work through some worksheet problems.
• Note: We will not be able to work through all
problems in the tutorial – it’s up to you to do that
on your own.
• Solutions will be provided by lecturers for all
problems, so you can check your answers.
• Email me if you have difficulty with any particular
problems.
In-Class Activity
• Split up into two (or three) teams.
• Each team will have a set of problems to do on
the board.
• Each team member do one problem.
• Teams can decide who goes first, problems can
be done in any order.
• Teammates can ask their team members for help
if they need it.
• Whichever team gets the most correct answers
first wins.
Activity – Solve for dy/dx
Team 1
Team 2
1. 𝑦 = 𝑥 3 − 4𝑥 5 + 10
2. 𝑦 = 𝑥 1/2 − 𝑥 −1/2 + 𝑥
3. 𝑦 =
2(3𝑥 2 ) 1/2 +𝑥 1/2
4. 𝑦 = 𝑥 −1/2 + (𝑥𝑧)1/2
5. 𝑦 =
4(𝑥 1/2
−
𝑥 3/4 )4 +4
6. 𝑦 = 𝑥 −7/8 + 𝑥 −3/4 + 2𝑥
7. 𝑦 = 4(5𝑥 2 )1/2 +3𝑥 2
8. 𝑦 = 2(𝑥 −1/3 + 𝑥 2 )3 +𝑥 2
1. 𝑦 = 𝑥 4 + 5𝑥 6 + 15
2. 𝑦 =
𝑥 3/4
1
2
− 𝑥 + 4𝑥 2
3. 𝑦 = 3(2𝑥 2 )1/2 −𝑥 −1/4
4. 𝑦 = 𝑥 3/4 − (𝑥𝑧 2 )1/2
1
5. 𝑦 = 3(𝑥
−2
+ 𝑥 2 )2 +𝑥
6. 𝑦 = 𝑥 2 − 7𝑥 4 + 24
7. 𝑦 = 2𝑥 1/2 + (𝑥 2 𝑧 4 )1/2
8. 𝑦 = 𝑥 −1/2 + (𝑥 3 𝑧 6 )1/3
Solutions (Team 1 problems)
1. 𝑦 = 𝑥 3 − 4𝑥 5 + 10
𝑑𝑦
= 3𝑥 2 − 20𝑥 4
𝑑𝑥
5. 𝑦 = 4(𝑥 1/2 − 𝑥 3/4 )4 +4
1
3 3 1
1
𝑑𝑦
3 −1
−2
2
4
= 16 𝑥 − 𝑥 ( 𝑥 − 𝑥 4 )
𝑑𝑥
2
4
2. 𝑦 = 𝑥 1/2 − 𝑥 −1/2 + 𝑥
𝑑𝑦 1 −1/2 1 −3/2
= 𝑥
− 𝑥
+1
𝑑𝑥 2
2
3. 𝑦 = 2(3𝑥 2 )
1/2 +𝑥 1/2
4. 𝑦 = 𝑥 −1/2 + (𝑥𝑧)1/2
1
𝑑𝑦
𝑑𝑥
7
= −8𝑥
−15
8
3
− 4𝑥
−7
4
+2
7. 𝑦 = 4(5𝑥 2 )1/2 +3𝑥 2
𝑑𝑦
1
= 2 3 + 𝑥 −1/2
𝑑𝑥
2
𝑑𝑦
𝑑𝑥
6. 𝑦 = 𝑥 −7/8 + 𝑥 −3/4 + 2𝑥
1
= − 2 𝑥 −3/2 + 2 𝑧 −1/2 𝑥 −1/2
𝑑𝑦
= 4 5 + 6𝑥
𝑑𝑥
8. 𝑦 = 2(𝑥 −1/3 + 𝑥 2 )3 +𝑥 2
3
𝑑𝑦
1 −4
−1
2
=6 𝑥 3+𝑥
− 𝑥 3 + 2𝑥 + 2𝑥
𝑑𝑥
3
Solutions (Team 2 problems)
1. 𝑦 =
𝑥4
+
5𝑥 6
1
5. 𝑦 = 3(𝑥
+ 15
𝑑𝑦
= 4𝑥 3 + 30𝑥 5
𝑑𝑥
2. 𝑦 = 𝑥
3/4
𝑑𝑦
𝑑𝑥
− 𝑥 + 4𝑥 2
6. 𝑦 = 𝑥 2 − 7𝑥 4 + 24
1
2
= 𝑥 −1/4 − 𝑥
−1
2
+ 8𝑥
3. 𝑦 = 3(2𝑥 2 )1/2 −𝑥 −1/4
𝑑𝑦
𝑑𝑥
1
+ 𝑥 2 )2 +𝑥
1
𝑑𝑦
1 −3/2
−2
2
= 6(𝑥 + 𝑥 )(− 𝑥
+ 2𝑥) + 1
𝑑𝑥
2
1
2
3
4
−2
= 3 2 + 4𝑥
−5
𝑑𝑦
= 2𝑥 − 28𝑥 3
𝑑𝑥
7. 𝑦 = 2𝑥 1/2 + (𝑥 2 𝑧 4 )1/2
4
4. 𝑦 = 𝑥 3/4 − (𝑥𝑧 2 )1/2
𝑑𝑦 3 −1/4 1 −1
= 𝑥
− 𝑧𝑥 2
𝑑𝑥 4
2
𝑑𝑦
= 𝑥 −1/2 + 𝑧 2
𝑑𝑥
8. 𝑦 = 𝑥 −1/2 + (𝑥 3 𝑧 6 )1/3
𝑑𝑦
𝑑𝑥
1
= − 2 𝑥 −3/2 + 𝑧 2
What can you do this week?
• Get the book and start reading for next week!
• Brush up on your calculus.
• Download the Week 2 worksheet and start
working on it – ask questions in the lecture if
you get stuck.
– Note: the week 2 worksheet is constrained
optimization and unconstrained optimization.