Need help with Math (on case in Consulting Bible)
Hey All - I've recently started doing cases out of WSO's Consulting Bible. If anyone has this, I'm having trouble with the math on Case 5 (Tommy's Tennis).
They want us to calculate what the new price should be given that there are 15 courts currently costing $20 an hour but there are 20 people that want to use the courts (ie excess demand of 5). We know that price elasticity is -1 (If the price of courts goes up by 10%, the number of people wanting to play will go down by 10%).
The formula they use to calculate what the new price should be is: New Price = [(% Change in Vol. / Elasticity) + 1] * Old Price New Price = [(-25% / -1) + 1]*$20 New Price = $20
Does anyone understand the math going on here? I think the -25% comes from 5/20 but I'm not sure why this formula works or what the intuition is. Any help would be much appreciated!
Is that right? I'm assuming the formula you have is "New Price = [(-25% / -1) + 1]$20 " or (1.25)20 which equals $25
not $20
ideally you want supply = demand. if you want demand to be 15 since supply is set, you have to reduce demand by 25% (5/20). since price is -1 elasticity, raise prices by 25% to cut demand by 25% to get $25 an hour.
sorry if i completely overlooked something, i dont have the case and that was my first intuition.
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