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Lecture 2

# Lecture notes week 2

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University of Toronto Scarborough

Economics for Management Studies

MGEA02H3

Gordon Cleveland

Fall

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1 Week 2: Demand and Supply in a Competitive Market NEWS FLASHES! th - Our first midterm test will be written on Saturday, October 17 at 5 pm (2 hour period with 90 minutes test) (less than 4 weeks away) - Tentative date for next midterm at Friday November 20 (3 to 5 pm) - More parts of Course Handbook are up on the UTSC Intranet - Tutorials start this weekschedule is on website, under ECMA04Professor and TAs - Office Hours for help from T.A.s in MW-369 are also up on website in same place (If you need helpgo get itTAs are paid to help you!) What did we learn last week? N definition of economics N opportunity cost N production possibilities model N calculating opportunity cost on PPF N PPF with increasing costs N maximizing a value (or utility) function along PPF Agenda for this week: N Overview of the competitive market model N What is a market? N What is competition? N Demand N Supply N Equilibrium N Shifts in Demand and Supply: how they affect equilibrium Dont 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). 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 + 4X = 400 or Y = [400 - 4X ] 0.5 Questions 1 through 3 concerns 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: ANSWER: dYdX = 0.5[400 - 4X ]2 -0(-8X) = -4X[400 - 4X ]2 -0.5 To get opportunity cost of X, use -dYdX, which is 4X[400 - 4X ] -0.5 0.5 Evaluate this expression at X = 6 to get the opportunity cost of X as = (4 x 6) (1[256] ) = 2416 = 32 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: www.notesolution.com 2 To get opportunity cost of Y, use -dXdY, or inverse of -dYdX. The opportunity cost of X is 4X[400 - 4X ] -0. When this expression is evaluated at X = 8, we have (4 x 8) (1[144] ) = 3212 = 83. We want the opportunity cost of Y which is the inverse or 38. 3. Suppose that those in charge of this economy want to maximize the utility of the residents of the 2 country, where utility can be computed according to the equation U = XY 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. So U = X[400 - 4X ] = 400X - 4X 3 Then set dUdX = 0 f2r maximum. dUdX = 400 12X = 0 or X = 5.774 www.notesolution.com

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