Topic_03_Elasticity_Estimation (1).pptm

# E dqdp c p c q 21 price elasticity of supply measures

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E = dQ/dP c * P c /Q.

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21 Price Elasticity of Supply Measures the percentage change in quantity supplied resulting from a 1 percent change in price. P Q E S S P % %
3.2 Regression Analysis A statistical technique to estimate the relationship between a dependent variable (such as quantity) and independent variable (such as price or income). When doing regression analysis, we put dependent variable on the left side of the equation and the explanatory variable on the right side. The relationship can be linear, quadratic or any other form. 22

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Regression Analysis Table 3.1 Data Used to Estimate Cod Demand at the Portland Fish Exchange Price in \$ per lb. Thousands of lbs 1.90 1.5 1.35 2.2 1.25 4.4 1.20 5.9 0.95 6.5 0.85 7.0 0.73 8.8 0.25 10.1 23
Cod Data in a Diagram We can estimate a demand curve by drawing a line or curve through these points. 24

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Using Regression to Estimate Demand We want to find the “best possible” line or curve that represents this data. In this example, whatever quantity of cod is brought to the market is sold on that day. Price adjusts to ensure that all quantity supplied is sold (or clear the market). Thus we think of price as the dependent variable and quantity explanatory or independent . But we can think the other way too. 25
Inverse Demand If we start with a standard demand curve of the form Q = a + bp (where b is negative), we can rearrange this expression to obtain p = -a/b + Q/b = g + hQ where g = -a/b and h = 1/b. This (p = -a/b + Q/b) is the inverse demand curve . It expresses the same information as the standard demand curve. 26

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Random Error When we observe actual data it would not normally lie on straight line. However, we can write: p = g + hQ + e where e is “random error”. The “error” shows the difference between the proposed linear relationship and the actual observation. The error might be due to non-price factors that we cannot hold fixed (such as random variations in the number of buyers who show up on a particular day) . 27
An Estimated Demand Curve The observed points do not lie on the estimated line precisely, because of the random error. 28

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Ordinary Least Squares The “residual” is the vertical distance between the actual price and the “predicted” price obtained from the regression line. We get our estimate of the demand curve by making the residuals small. An “ ordinary least squares (OLS) ” method makes the sum of squared residuals as small as possible. This is normally done using computer programs such as Excel. 29
Trendline 30 1 2 3 4 5 6 7 8 9 10 11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f(x) = - 0.15x + 1.95 R² = 0.91

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Question: Effect of Changing Price 31 The R 2 number shows how well the estimated regression line fits the data. Thus the R 2 statistic measures the goodness of fit . If R 2 = 1, then all the observed points lie on the estimated line and hence the estimated regression line perfectly fits the data.
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