101 Class 13 W2008 - Principles of Economics I Economics...

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Unformatted text preview: Principles of Economics I Economics 101 Announcements Readings: CTools notes Chapter 6 Discussion Sections this week New assignment available this afternoon Quiz in section this week Qd = a + b P P Demand Slope = 1/b P0+1 P0 1 b Q0b Q0 a0 a1 Q A more general model of demand Again, use a linear specification for simplicity: Qd = b0 + b1 P + b2 Psub + b3 Pcomp + b4 Y + b5 Pop + ... Where: P = own price of the good Psub = price of a substitute Pcomp = price of a complement Y = income (e.g. average household income) Pop = population etc A more general model of demand Rearranging the same expression: Q = [b + b P + b P + b Y + b Pop + ...] + b P d 0 2 sub 3 comp 4 5 1 = a + b1 P where a = [b0 + b2 Psub + b3 Pcomp + b4 Y + b5 Pop + ...] i.e. changes in demand determinants other than own price will simply change the Qaxis intercept Call these "demand shifters" or "shift variables" Substitutes and Complements If an increase in price of good A increases demand for good B, then good A is a substitute for good B Implication is that the coefficient in front of PA in the good B demand function must be positive An increase in P increases the Qaxis intercept of A the demand curve i.e. shifts it to the right Substitutes and Complements If an increase in price of good A decreases demand for good B, then good A is a complement for good B Implication is that the coefficient in front of PA in the good B demand function must be negative An increase in P decreases the Qaxis intercept of A the demand curve for good B i.e. shifts it to the left Normal and Inferior Goods If an increase in income increases demand for good B, then good B is normal Implication is that the coefficient in front of Y in the good B demand function must be positive An increase in Y increases the Qaxis intercept of the demand curve for good B i.e. shifts it to the right Normal and Inferior Goods If an increase in income decreases demand for good B, then good B is inferior Implication is that the coefficient in front of Y in the good B demand function must be negative An increase in Y decreases the Qaxis intercept of the demand curve for good B i.e. shifts it to the left Estimating the Demand Curve Suppose we gather some data: Pricequantity observations (Pi, Qi) Maybe the same market in different periods i.e. at price Pi, the quantity demanded was Qi Time series data Maybe different (but similar) markets at the same time Maybe different (but similar) markets at various times Crosssectional data Panel data Can we use this data to infer what the demand function is like? P P1 1 P2 P3 P4 2 3 4 P5 5 Q1 Q2 Q3 Q4 Q5 Q Ordinary least squares estimation Suppose we knew (or believed) the demand function to have the form Qd = a + b P + a + b P : deterministic (predictable) variation in Qd : random (unpredictable) variation in Qd This term explains why the data don't look like they fall on a linear demand curve P P1 1 Qd = a + b P P2 P3 P4 P5 5 a Q 4 2 But we don't know the deterministic portion of the model We must estimate the demand curve, using the information available i.e. observed price-quantity pairs ^ ^ ^ Q( P) = a + b P Estimated function: ^ ^ Where ( a > 0 and b < 0 ) P e1 Residuals e3 P1 P2 P3 P4 e4 P5 Slope = 1 ^ b Q ^ a Residuals Residual: ^ ei = Qi - Q( Pi ) Measure of how inaccurate the estimate is Wish to choose the estimated function to make the residuals small What does that mean? In previous diagram, making the curve steeper will make some residuals bigger and some smaller. Is this good? P Sum of Residuals e3 = 50 3 30 20 2 10 1 e1 = - 50 Q 100 150 200 300 ...
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