---

Overview

Title
Point Ealsticity
Elasticity and TR
Graph TR
Arc Elasticity

---

Sheet 1: Title

								© R Larry Reynolds - 1999

---

Sheet 2: Point Ealsticity

Elasticity is a measure of responsiveness of a dependent variable to changes in an independent variable. "Own" price elasticity of demand or just price elasticity is a measure of the responsiveness of buyers of a good to changes in the price of that good. It is a ratio of the percentage change in quantity to a percentage change in price. Point price elasticity can be calculated at any price by multiplying the slope of the demand function (b) times the P/Q, when Q = a - bP While price elasticity is obviously related to demand, it is also related to revenue obtained from the sale of the good considered. Elasticity		Change intercepts		Given a demand function:		Q =	49	-	2,3	P	© R Larry Reynolds 1999
This Excel Spreedsheet allows you to diplay the coefficient of price elasticity of demand for any price and quantity on a linear demand function. You can select the demand function by altering the intecept and slope of the demand equation using the control buttons to increase or decrease the values. The control buttons directly above the price (P1) will change the price in increments of $.10 For any demand function, enter a price and the point elasticity will be diplayed. Instructions				Which can be written:		P =	21,304347826087	-	0,434782608695652	Q
Demand Function
Price	Quantity
$25,00	-8,49999999999999
$24,00	-6,2	Price elasticity of demand is determined by the slope of the demand function and the location on the demand function. For a linear demand function the slope is the same at each price and quantity but the location changes, therfore, the point price elasticity will be different at each price. The next Excel sheet will show the price elasticity at each price and its relationship to total revenue (TR). "Point" price elasticity
$23,00	-3,9
$22,00	-1,59999999999999	At a price, P =		$12,30
$21,00	0,700000000000003	Quantity is Q =		20,71
$20,00	3			Note that the slope of the line in the graph is the reciprocal of the slope (b) in the equation Q = a - bP The slope of demand function in the graph (which is written P = f(Q) ) will have a slope -(1/b) About slope
$19,00	5,3	Slope of Q = f (P) =		-2,3
$18,00	7,6	Ratio of P /Q =		0,59
$17,00	9,90000000000001	Try to find the price and quantity that has a coefficient of elasticity = -1 This is unitary elasticity. Find the range of prices (and quantities) where the absolute value of elasiticity is greater than 1. Find where the absolute value is less than 1. Questions
$16,00	12,2
$15,00	14,5
$14,00	16,8	At price P =		$12,30
$13,00	19,1	Point price elasticity =		-1,3660
$12,00	21,4	A 1% change in price will cause a
$11,00	23,7	1,37%	change Q demanded
$10,00	26
$9,00	28,3
$8,00	30,6	© R Larry Reynolds - 1999
$7,00	32,9
$6,00	35,2
$5,00	37,5
$4,00	39,8				$12,30	20,71
$3,00	42,1				$12,30	0
$2,00	44,4				0	20,71
$1,00	46,7					20,71
$0,00	49

---

Sheet 3: Elasticity and TR

Total Revenue (TR) is defined as price times quantity. Elasticity is defined as a ratio of the percentage change in quantity to the percentage change in price. Since TR and elasticity are both functions of price and quantity, they are related. TR will be a maximum when the coefficient of price elasticity = -1 or is at "unitary elasticity." Revenue	Change the slope and intercept values with control buttons below.						Q =	59	-	2,3	P
This Excel Spreedsheet will allow you to select a slope and an intecept for a demand function. The coefficient of price elasticity and revenue functions will be diplayed in the table for each price. Change ether or both the slope and intercept of the demand function using the control buttons. Given the demand function you select, the total revenue (TR), average revenue (AR) and marginal revenue (MR) will be displayed at each price. Note the values for AR are the same as the prices. AR will always be the same as price. Red cells appear when Quantity is negative. Instructions					Which can be written:		P =	25,6521739130435	-	0,434782608695652	Q
Demand is typically defined as a schedule of quantities that individuals are willing and able to purchase at a schedule of prices in a given period of time under constant conditions. Q = f(P) Demand can also be thought of as the maximum prices (reservation prices) that buyers are willing to pay for each unit of the good. P = f(Q) Demand Function		Price elasticity of demand is a ratio of the percentage change in quantity caused by a percentage change in price. Point price elasticity is calculated by multiplying the slope of the demand function by a ratio of price over quantity. Remember that the slope in the demand function expressed Q = a - bP is not the apparent slope when demand is graphed with price on the vertical axis and quantity on the horizontal axis. Point price elasticity will be different at every price. Elastic When the absolute value of price elasticity is greater than 1, demand is said to be "elastic." % change in quantity > % change in price. TR will fall as price increases. Inelastic If the absolute value of price elasticity is less than 1, demand is said to be "inelastic." % change in quantity < % change in price. TR will rise as price increases. Point Price Elasticity	Revenue Functions
Price	Quantity		Total Revenue (TR) is defined as price times quantity. TR = PQ TR	AR is calculated as TR/Q. Since TR = PQ, PQ/Q = P AR is the revenue per unit sold AR	Marginal Revenue is calculated as the first derivative of the TR function, When P = a - bQ then TR = (a - bQ)Q = aQ-bQ^2 Therefore, MR = a -2Q In principles the MR may be calculated as the TR at a quantity minus the TR for the previous quantity. MR is the change in TR caused by a one unit change in the quantity sold. MR'
$25,00	1,50000000000001	-38,33	$37,50	$25,00	24,3478260869565
$24,00	3,8	-14,53	$91,20	$24,00	22,3478260869565
$23,00	6,1	-8,67	$140,30	$23,00	20,3478260869565
$22,00	8,40000000000001	-6,02	$184,80	$22,00	18,3478260869565
$21,00	10,7	-4,51	$224,70	$21,00	16,3478260869565
$20,00	13	-3,54	$260,00	$20,00	14,3478260869565
$19,00	15,3	-2,86	$290,70	$19,00	12,3478260869565
$18,00	17,6	-2,35	$316,80	$18,00	10,3478260869565
$17,00	19,9	-1,96	$338,30	$17,00	8,34782608695652	What are the relationships of MR and elasticity to the maximum value of TR?
$16,00	22,2	-1,66	$355,20	$16,00	6,34782608695652
$15,00	24,5	-1,41	$367,50	$15,00	4,34782608695652
$14,00	26,8	-1,20	$375,20	$14,00	2,34782608695652	The maximum TR is approximately
$13,00	29,1	-1,03	$378,30	$13,00	0,34782608695652			$378,30
$12,00	31,4	-0,88	$376,80	$12,00	-1,65217391304348	(The number may not be precisely the maximum because the prices change in increments of $1)
$11,00	33,7	-0,75	$370,70	$11,00	-3,65217391304348
$10,00	36	-0,64	$360,00	$10,00	-5,65217391304348
$9,00	38,3	-0,54	$344,70	$9,00	-7,65217391304348			© R Larry Reynolds 1999
$8,00	40,6	-0,45	$324,80	$8,00	-9,65217391304348
$7,00	42,9	-0,38	$300,30	$7,00	-11,6521739130435
$6,00	45,2	-0,31	$271,20	$6,00	-13,6521739130435
$5,00	47,5	-0,24	$237,50	$5,00	-15,6521739130435
$4,00	49,8	-0,18	$199,20	$4,00	-17,6521739130435
$3,00	52,1	-0,13	$156,30	$3,00	-19,6521739130435
$2,00	54,4	-0,08	$108,80	$2,00	-21,6521739130435
$1,00	56,7	-0,04	$56,70	$1,00	-23,6521739130435
$0,00	59	0,00	$0,00	$0,00	-25,6521739130435
			$378,30

---

Sheet 4: Graph TR

Elasticity is a measure of responsiveness of a dependent variable to changes in an independent variable. "Own" price elasticity of demand or just price elasticity is a measure of the responsiveness of buyers of a good to changes in the price of that good. It is a ratio of the percentage change in quantity to a percentage change in price. While price elasticity is obviously related to demand, it is also related to revenue obtained from the sale of the good considered. Elasticity	Use spinner control to change intecept and slope of demand					Q =	25	-	0,64	P			64
This Excel Spreedsheet allows you to diplay the average or "arc" coefficient of price elasticity of demand for any set of prices and quantity on a linear demand function. You can select the demand function by altering the intecept and slope of the demand equation using the control buttons to increase or decrease the values. Arc elasticity is an average elasticity. You must enter two prices (which yields a quantity associated with each price). Arc elasticity is the average elasticity of the demand function between the two prices. Economists typically refer to elasticities rather than demand functions. The coefficient of elasticity they refer to is an average elasticity in the normal price range for the good. Instructions				This function can be written:		P =	39,0625	-	1,56	Q
Demand Function		Total Revenue	Point Elasticity	Marginal Revenue
Price	Quantity
$40,00	-0,60	-$24,00	42,67	$40,94
$39,00	0,04	$1,56	-624,00	$38,94
$38,00	0,68	$25,84	-35,76	$36,94
$37,00	1,32	$48,84	-17,94	$34,94
$36,00	1,96	$70,56	-11,76	$32,94
$35,00	2,60	$91,00	-8,62	$30,94
$34,00	3,24	$110,16	-6,72	$28,94
$33,00	3,88	$128,04	-5,44	$26,94
$32,00	4,52	$144,64	-4,53	$24,94
$31,00	5,16	$159,96	-3,84	$22,94
$30,00	5,80	$174,00	-3,31	$20,94
$29,00	6,44	$186,76	-2,88	$18,94
$28,00	7,08	$198,24	-2,53	$16,94
$27,00	7,72	$208,44	-2,24	$14,94
$26,00	8,36	$217,36	-1,99	$12,94
$25,00	9,00	$225,00	-1,78	$10,94
$24,00	9,64	$231,36	-1,59	$8,94
$23,00	10,28	$236,44	-1,43	$6,94
$22,00	10,92	$240,24	-1,29	$4,94	The maximum TR is approximately
$21,00	11,56	$242,76	-1,16	$2,94			$244,00
$20,00	12,20	$244,00	-1,05	$0,94
$19,00	12,84	$243,96	-0,95	-$1,06	© R Larry Reynolds 1999
$18,00	13,48	$242,64	-0,85	-$3,06
$17,00	14,12	$240,04	-0,77	-$5,06
$16,00	14,76	$236,16	-0,69	-$7,06
$15,00	15,40	$231,00	-0,62	-$9,06
$14,00	16,04	$224,56	-0,56	-$11,06
$13,00	16,68	$216,84	-0,50	-$13,06
$12,00	17,32	$207,84	-0,44	-$15,06
$11,00	17,96	$197,56	-0,39	-$17,06
$10,00	18,60	$186,00	-0,34	-$19,06
$9,00	19,24	$173,16	-0,30	-$21,06
$8,00	19,88	$159,04	-0,26	-$23,06
$7,00	20,52	$143,64	-0,22	-$25,06
$6,00	21,16	$126,96	-0,18	-$27,06
$5,00	21,80	$109,00	-0,15	-$29,06
$4,00	22,44	$89,76	-0,11	-$31,06
$3,00	23,08	$69,24	-0,08	-$33,06
$2,00	23,72	$47,44	-0,05	-$35,06
$1,00	24,36	$24,36	-0,03	-$37,06
$0,00	25,00	$0,00	0,00	-$39,06
		$244,00

---

Sheet 5: Arc Elasticity

Elasticity is a measure of responsiveness of a dependent variable to changes in an independent variable. "Own" price elasticity of demand or just price elasticity is a measure of the responsiveness of buyers of a good to changes in the price of that good. It is a ratio of the percentage change in quantity to a percentage change in price. While price elasticity is obviously related to demand, it is also related to revenue obtained from the sale of the good considered. Elasticity		Change intercepts		Given a demand function:		Q =	42	-	1,8	P
This Excel Spreedsheet allows you to diplay the average or "arc" coefficient of price elasticity of demand for any set of prices and quantity on a linear demand function. You can select the demand function by altering the intecept and slope of the demand equation using the control buttons to increase or decrease the values. Arc elasticity is an average elasticity. You must enter two prices (which yields a quantity associated with each price). Arc elasticity is the average elasticity of the demand function between the two prices. Economists typically refer to elasticities rather than demand functions. The coefficient of elasticity they refer to is an average elasticity in the normal price range for the good. Instructions				Which can be written:		P =	23,3333333333333	-	0,555555555555556	Q
Demand Function
Price	Quantity
$25,00	-3
$24,00	-1,2	Select two prices, P1, P2
$23,00	0,600000000000001	P1 =	$12,80
$22,00	2,4		Then, Q1 =	18,96
$21,00	4,2
$20,00	6	P2 =	$10,90
$19,00	7,8	then	Q2 =	22,38
$18,00	9,6	Given P1 and P2, the
$17,00	11,4
$16,00	13,2	Percentage change in Q =		-18,038%
$15,00	15	Percentage change in P =		14,844%
$14,00	16,8		Arc elasticity is the "average elasticity" at each point along a line between two prices. Since the percentage change in P or Q is calculated at a point, Arc Elasticity is not the % change in Q / % change in P at any specific point on the demand function. Arc Elasticity
$13,00	18,6	Arc Elasticity between P1 and P2
$12,00	20,4	is	-1,032
$11,00	22,2
$10,00	24
$9,00	25,8
$8,00	27,6
$7,00	29,4
$6,00	31,2								© R Larry Reynolds 1999
$5,00	33
$4,00	34,8		109	$12,80	18,96
$3,00	36,6		128	$10,90	22,38
$2,00	38,4	$12,80	18,96	$10,90	22,38
$1,00	40,2	0	18,96	0	22,38
$0,00	42	$12,80	0	$10,90	22,38
		$12,80	18,96	$10,90	0