Hello again. before we put the information we just learned about price elasticity of demand [UNKNOWN] use, a little aside as to how we calculate this price elasticity of demand. There are two ways that economists use. One's called the point elasticity formula, one's called the arc elasticity formula. And what you'll see on page ten of these PowerPoints is, the difference is, how you scale the changes in quantity and the changes in price. What you use to scale by. In the case of the point elasticity formula, we look at the change in quantity demanded in the numerator and we scale by a particular point. We scale by the initial demand point d1, or we scale by the ending demand point, d2. So we can do two different versions of the point elasticity formula using, either using the final of price quantity combination or the initial price quantity combination. And that's what's presented in those two depictions of ADA, under those point elasticity formula,. Arc elasticity uses an average, and says look, don't pick a particular point, but let's just average across the beginning and ending points. And so, in the numerator we scale the change in quantity demanded by the average of the initial and final quantity demanded. Similarly, we scale the change in price by the average of the initial and final price. Does it make a difference, which formula we use? It turns out for fairly small changes in price and quantity, it doesn't make much of a difference. But for larger changes, the average or the Arc elasticity formula provides a more reliable number. And to test this out, let me just give you an example. Let's say initially, the price of gasoline was $3.00 and we sold a thousand units per time period. And then the price gets lowered to a buck 50. And we sell more 2,000 units per period. Test yourself on this. But if, if we use the point elasticity formula, scaling by the initial point, the P1 of $3, and the QD1 of 1000, you'd calculate the point elasticity to be two in absolute value terms. If you calculate it using the final price and quantity demanded combination, you'd end up with an estimate of 0.5. The true estimate lies in between these, and that's what the arc formula reveals. For a fairly large change in price, so price getting cut in half from $3 to $1.50. The arc elasticity will give you a more reliable estimate. So in, what the arc elasticity, if you do the calculation, and you should test yourself on this, will show you, it's no, it's a unitary elasticity of one. So, I would encourage you to, to check the math out to make sure you're following along. In practical terms. let's say we have a small increase in price in oil markets, something's changed in a place like Nigeria or China. If it's just a small increase in price, then it won't matter if we use the point elasticity or the arc test to make what'll happen to quantity demanded. However, if there's a major disruption in a place like Algeria or a place like, Syria or Iraq or Iran, then arc elasticity if there's an expected major increase in price, arc elasticity will give us a better estimate. Examples of how you apply elasticity of demand. Let me give you one in particular from cable television. Cable television consists of basic tiers as well as paid tiers. Basic tiers involve re-transmitted local broadcast signals. certain also satellite services such as CNN Headline News, certain sports channels. Up through 1990, basic tiers were regulated by governments. There were limits on how much you could charge for basic tier. Paid tier services by contrast, there are no limits. In 1990, deregulation occurred, and so cable operators had to figure out should we raise rates, keep them the same, or potentially lower them. And what they found out is, based on the elasticities we calculated or, or calculated at the time that they were charging too low a price for basic rates. They determine through some sophisticated analysis, that the price elasticity of demand was on the order of 0.2 to 0.5. It was inelastic. What that indicated is that if we raise price by 10%, quantity demand would only go down only by 2 to 5%. So quantity demand wasn't as responsive as any given change, percentage change in price. And any time you have a situation where you're producing a product, that you estimate elasticity, price elasticity of demand to be less than 1, you're charging too low a price. And let's see why by flipping back to diagram figure, figure 2.9. Inelastic demand was our middle case. was a case where it, prior we were looking at lowering the price from $3 to 1.50. If we do it in reverse though, when we raise price, total expenditures will go up, will go in the same direction that price goes. So anytime demand is inelastic, price and total expenditures go together. So let's just say hypothetically in the cable TV cases, the core price for basic tier is $1.50. If you raise price, in a, in a situation where we had in elastic demand, you, you would pick up a larger rectangle in the form of L then you would lose in the lost sales of G. So anytime demand is inelastic, price is going to push total expenditures with it. In addition to increasing your revenues by raising price, you also lower your cost. So profits will go up not just because revenues go up, but cost goes down as you have more subscribers, as you have fewer subscribers that you need to service. Quality demanded falls in this case from 120 to 100. Higher revenue, lower cost, mean greater profits. And no surprise, cable operators over the next few years post deregulation raise basic tier rates an average of 75%. Drives home the point. Any time demand is in elastic, price inelastic, your price is too low as a producer. How about if we have a case like figure 2.9a? Should you look, raise or lower your price? This one's trickier. If you face elastic demand, raising your price will mean that you'll pick up less in revenue than you'll lose in quantity. The quantity has a bigger effect, the denominator, sorry, the numerator of the elasticity formula quantity has a bigger impact when the ratio of the quantitative to price impact's greater than one. When elasticity, when demand is elastic. So, instincts would be, let's try to lower price because we'll pick up more in quantity. We'll add more to sales that way. Why it's unclear though is, while you pick up more in revenue by lowering price, you also pick up more in cost. You raise total cost because you have more consumers now to serve. So the correct answer of demand is elastic will depend on how much you add to revenue, as we'll see in a later session, relative to how much you add to cost. What if demand has unitary elasticity, price elasticity of demand is exactly equal to one, like figure 2.9c? There, you should definitely raise your price. Why? When you raise price, let's say we go from $1.50 to $3. We'll pick up as much in price per unit, the L rectangle, as we lose in sales, the G rectangle. So total revenue will stay the same by raising price. The quantity and price effects exactly counter balance each other. The numerator has the same impact as the denominator in the price elasticity formula. But profits will go up, because you will have fewer customers, lower costs. So same revenue at a higher price, lower total cost, more profit. And so as a cable operator or producing any other product, if you ever estimate your price elasticity of demand to be unitary, you're charging too low a price. [BLANK_AUDIO]
