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Unformatted text preview: ill this PDS profit? ↓ Options by $200 ↑ by 30% Why might and will this PDS profit? ↑ Promotion ↑ by 30% Why might and will this PDS profit? Reduce Operations to: 16 hours weekdays & 8 hours Saturday ↓ by 20% Why might and will this PDS profit? As we are about to see, in order to analyze each of these options we will need to know PDS’s as well as the equation of the function (think about this: we need to guess the equation of the function and then estimate its parameters!). We will use “regression analysis” to “guesstimate” the “functional form” of the cost function equation and estimate its parameters. We illustrate regression analysis by an example: back in lectures 1 and 2 we derived the commercial 30 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. demand curve “by hand” by noting that according to the managerial opinions in the case, the commercial demand curve had to be linear (why?): We argued that the demand curve is linear: $1,466.66 $1,000 We can solve for and by substituting any two pairs of and solving the simultaneous equations: $800 $600 (0.7)138 138 (1.3)138 However, if the three points are not literally on a straight line then we can’t derive the demand equation “by hand”. For example, in March 2003 where now suppose management thinks that raising price by $200 will reduce demand by 16% and lowering price by $150 will increase demand by 35% (see graph below): It “looks like” these 3 points are more or less around a straight line. We can use Excel to estimate the parameters of our guesstimated linear demand curve. Click on any data point right click on any data point Choose “Add Trendline” 31 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. A menu pops up: since we think the demand curve is linear, choose the “linear” fit and choose “show equation”: Click OK and now Excel graphs the “best fitting linear” line through the scatterplot and gives you its equation: 32 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The “y” variable is and the “x” variable is so that equation of this “linear” demand curve is: With this, let’s estimate the cost function but first let’s argue why we need the cost function. In the following table notice that PDS’s losses are becoming smaller over time due to more commercial hours billed (assuming that average intercompany hours are 205/month (where did we get this figure?)): From Exhibits 1 and 2 in The Prestige Telephone Company Prices are $/hour January February March Intercompany Hours 206 181 223 Intercompany Price $400 $400 $400 Commercial Hours 123 135 138 Com...
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