Week2.DemandandSupply.2009

Week2.DemandandSupply.2009 - 1 Week 2 Demand and Supply in...

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1 Week 2: Demand and Supply in a Competitive Market NEWS FLASHES! - Our first midterm test will be written on Saturday, October 17 th (less than 4 weeks away) - More parts of Course Handbook are up on the UTSC Intranet - Tutorials start this week…schedule is on website, under ECMA04/Professor and TAs - Office Hours for help from T.A.s in MW-369 are also up on website in same place (If you need help…go get it…TAs are paid to help you!)
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2 What did we learn last week? - definition of economics - opportunity cost - production possibilities model - calculating opportunity cost on PPF - PPF with increasing costs - maximizing a value (or utility) function along PPF
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3 Agenda for this week: - Overview of the competitive market model - What is a market? - What is competition? - Demand - Supply - Equilibrium - Shifts in Demand and Supply: how they affect equilibrium Don’t forget your tutorials this week. And our 6 new T.A.’s have office hours! Leslie, Juan, Lisa, Zuoyi, Sam and Shoeb (check www.utsc.utoronto.ca/~cleveland for the time of office hours in MW-369 and the time and location of tutorials. Click on the button for ECMA04 and then on the button on the right-hand side for “Professor and TAs”).
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4 Use questions from a test in previous years to review material on opportunity cost and PPF. 1-3. A country produces goods X and Y and has the following equation for its production possibilities frontier: Y 2 + 4X 2 = 400 or Y = [400 - 4X 2 ] 0.5 Questions 1 through 3 concern this country. 1. You are told that the economy is producing efficiently and has chosen to produce and consume 6 units of X and 16 units of Y. At this point on the production possibilities frontier, you can use calculus to obtain the opportunity cost of X as:
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5 ANSWER: dY/dX = 0.5[400 - 4X 2 ] -0.5 (-8X) = -4X[400 - 4X 2 ] -0.5 To get opportunity cost of X, use -dY/dX, which is 4X[400 - 4X 2 ] -0.5 Evaluate this expression at X = 6 to get the opportunity cost of X as = (4 x 6) (1/[256] 0.5 ) = 24/16 = 3/2
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6 2. Now you are told that the economy is producing efficiently and has chosen to produce and consume 8 units of X. At this point on the production possibilities frontier, you can use calculus to obtain the opportunity cost of Y as: ANSWER: To get opportunity cost of Y, use -dX/dY, or inverse of -dY/dX. The opportunity cost of X is 4X[400 - 4X 2 ] -0.5 . When this expression is evaluated at X = 8, we have (4 x 8) (1/[144] 0.5 ) = 32/12 = 8/3. We want the opportunity cost of Y which is the inverse or 3/8.
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7 3. Suppose that those in charge of this economy want to maximize the utility of the residents of the country, where utility can be computed according to the equation U = XY 2 The point on the PPF that will maximize the value of the output involves the production of how many units of X (rounding to two decimal places)? ANSWER: We need to find the point which satisfies both the utility function and the production possibilities function. Substitute the PPF, expressed in terms of Y, into the utility (or value) function.
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