ECON 220 Week 1 Introductions • • • • • 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 5. 𝑦 = 3(𝑥 1 −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 𝑑𝑦 1 = 2 3 + 𝑥 −1/2 𝑑𝑥 2 4. 𝑦 = 𝑥 −1/2 + (𝑥𝑧)1/2 𝑑𝑦 𝑑𝑥 1 1 = − 2 𝑥 −3/2 + 2 𝑧 −1/2 𝑥 −1/2 6. 𝑦 = 𝑥 −7/8 + 𝑥 −3/4 + 2𝑥 𝑑𝑦 𝑑𝑥 7 = −8𝑥 −15 8 3 − 4𝑥 −7 4 +2 7. 𝑦 = 4(5𝑥 2 )1/2 +3𝑥 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 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 1 −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.