Consumption- Dead and supply pius 1s a would need to be given, in order to be just willing to give up their entire consumption of a particular good. Consumer is approximately the area behind the demand curve. The change in consumer surplus following a rice change is illustrated in the second graph △R nly pays P* Irve shows how much the consumer values each consecutive unit of the good. The consumer actually for each unit. Hence consumer surplus is the difference between what the consumer is willing to pay and what they actually pay. Denand and Supply Compensating and Equivalent variation Two more accurate(but harder to calculate)measures of the loss or gain to a consumer following a price change are compensating wariation and equivalent wariation. These are based on the Hicks decomposition. Price inc - the budget line gets steeper. Choice alters from r to r2 Equivalent variation (EV) in the first graph is the amount of money income which would have to be taken away from the consumer in order to put them on their new indifference curve. Compensating variation(CV) in the second graph is the amount of money income required to p ack on their initial indifference -the money needed to compensate for the pr For quasi-linear preferences: CV= EL surplus
Consumption — Demand and Supply 1 Consumer Surplus • Consumer surplus is a measure of how much money a consumer would need to be given, in order to be just willing to give up their entire consumption of a particular good. • Consumer surplus is approximately the area behind the demand curve. The change in consumer surplus following a price change is illustrated in the second graph. ................................................................................................................................................................................................................................................................................ .................................................................................................................................................................................................................................................................................. . . ............................................................................................................. ................................................................................................................................................................... ....................................................... 0 0 p x p x p ∗ x ∗ p ∗ 1 x ∗ 1 x ∗ 2 p ∗ 2 R ∆R . . . . . . . . . . . . . . • The demand curve shows how much the consumer values each consecutive unit of the good. The consumer actually only pays p ∗ for each unit. Hence consumer surplus is the difference between what the consumer is willing to pay and what they actually pay. Consumption — Demand and Supply 2 Compensating and Equivalent Variation • Two more accurate (but harder to calculate) measures of the loss or gain to a consumer following a price change are compensating variation and equivalent variation. These are based on the Hicks decomposition. . ............................................................................... . .................................................................................................... . ............................................................................... . .................................................................................................... ............................................................................................................................................................................................................................................................................................. . . ............................................................................................................................................................................................................................................................................................. . . . . . . . . . 0 x2 x1 • • • • • 0 x2 x1 • • • • • EV x x 1 2 CV x 1 x 2 • Price increases — the budget line gets steeper. Choice alters from x 1 to x 2 . • Equivalent variation (EV ) in the first graph is the amount of money income which would have to be taken away from the consumer in order to put them on their new indifference curve. • Compensating variation (CV ) in the second graph is the amount of money income required to put the consumer back on their initial indifference curve — the money needed to compensate the consumer for the price change. • For quasi-linear preferences: CV = EV = consumer surplus
Consumption- Dead and supply Producer Surplus Producer surplus, PS, is a measure of how much money a producer would need to be given, in order to be just Hilling to give up their entire supply of a particular good. Producer surplus is the area behind the supply curve. The change in producer surplus following a price change is illustrated in the second graph. 1 The supply curve shows how much each consecutive unit of the good costs the producer. The producer actually gets p*for each unit. Producer surplus is the difference between what it costs to make each unit and the actual price. Denand and Supply Market demand To obtain market demand for good 1 from individual demands, simply add them all X1(p1,P2 )=∑式(P2,P,m) The demand curve is written D(P) and will look something like this: D(P) X The inverse demand function P(X)is often used, and is simply calculated by finding price in terms of quantities from D(P). It measures the marginal rate of substitution of every consumer purchasing the good. ote aggregate demand is a function of all other prices and incomes. It will shift given a change in these variables example. if the good is normal and there is an increase in income levels it will shift to the right Adding each individuals urplus gives the market behind the demand curve
Consumption — Demand and Supply 3 Producer Surplus • Producer surplus, PS, is a measure of how much money a producer would need to be given, in order to be just willing to give up their entire supply of a particular good. • Producer surplus is the area behind the supply curve. The change in producer surplus following a price change is illustrated in the second graph. ................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................. ............................................................................................................. ................................................................................................................................................................... ....................................................... 0 0 p x p x p ∗ x ∗ p ∗ 1 x ∗ 1 x ∗ 2 p ∗ 2 PS ∆PS . . . . . . . . . . . . . . . • The supply curve shows how much each consecutive unit of the good costs the producer. The producer actually gets p ∗ for each unit. Producer surplus is the difference between what it costs to make each unit and the actual price. Consumption — Demand and Supply 4 Market Demand • To obtain market demand for good 1 from individual demands, simply add them all up: X1(p1, p2; m1, . . . , mn) = Xn i=1 x i 1 (p1, p2, mi) • The demand curve is written D(P) and will look something like this: ................................................................................................................................................................................................................................................................................ . .......................................................................................................................... 0 P X CS D(P) P ∗ X∗ . . . . . • The inverse demand function P(X) is often used, and is simply calculated by finding price in terms of quantities from D(P). It measures the marginal rate of substitution of every consumer purchasing the good. • Note aggregate demand is a function of all other prices and incomes. It will shift given a change in these variables. For example, if the good is normal and there is an increase in income levels it will shift to the right. • Adding each individual’s consumer surplus gives the market consumer surplus. The area behind the demand curve
Consumption- Dead and supply Elasticities · The slope of the demand curve is△ easure of the responsiveness of demand to prices. However, it depends upon the units demand and price are measured in The price elasticity of demand does not. It is written n and given br emanded dP % Change in price This is negative, so absolute values are often taken. If the result is 1. there is unit elasticity. If it is less than 1 inelastic. otherwise it is elastic. Consider the linear demand curve P= 1-X. Elasticity is given by n=-P/(1-P). This is not constant along the curve- it ranges from -oo at the vertical axis, through -l at P= 0.5 to O at the X axis. m-m Ar s dr- change in quantity demanded dn If Tn >0 the good is normal, if not it is inferior. If nm >I the good is a luxury Denand and Supply Revenue Revenue is the quantity of the good sold times its price: R=PX R'=(X+△X)(P+△P. Multiplying this out gives:F"=Px+P△X+X△P+△P△X. Subtracting one from the other gives△R=R-R=P△X+X△P+△P△x. The last term is tiny.So Marginal revenue the additional revenue from a small increase in quantity is: For the linear case then MR=P(l-(1-P)/P)=P-(1-P)=2P-1=1-2x
Consumption — Demand and Supply 5 Elasticities • The slope of the demand curve is ∆X/∆P. This is a measure of the responsiveness of demand to prices. However, it depends upon the units demand and price are measured in. • The price elasticity of demand does not. It is written η and given by: η = P X ∆X ∆P ≈ P X dX dP = %Change in quantity demanded %Change in price • This is negative, so absolute values are often taken. If the result is 1, there is unit elasticity. If it is less than 1 demand is inelastic, otherwise it is elastic. • Consider the linear demand curve P = 1 − X. Elasticity is given by η = −P/(1 − P). This is not constant along the curve — it ranges from −∞ at the vertical axis, through −1 at P = 0.5 to 0 at the X axis. • Elasticities can be found for other variables, for example the income elasticity of demand is: ηm = m x ∆x ∆m ≈ m x dx dm = %Change in quantity demanded %Change in income • If ηm ≥ 0 the good is normal, if not it is inferior. If ηm > 1 the good is a luxury. Consumption — Demand and Supply 6 Revenue • Revenue is the quantity of the good sold times its price: R = P X. • If a small amount more, X + ∆X, is sold at a slightly different price P + ∆P, the new revenue becomes R0 = (X + ∆X)(P + ∆P). Multiplying this out gives: R0 = P X + P ∆X + X∆P + ∆P ∆X. • Subtracting one from the other gives ∆R = R0 − R = P ∆X + X∆P + ∆P ∆X. The last term is tiny. So: • Marginal revenue — the additional revenue from a small increase in quantity is: MR = ∆R ∆X = P + X ∆P ∆X ≈ P + X dP dX = P µ 1 − 1 |η| ¶ • For the linear case then MR = P(1 − (1 − P)/P) = P − (1 − P) = 2P − 1 = 1 − 2X
Consumption- Dead and supply Marginal Revenue Curve The first graph shows linear demand P=1-X. The marginal re curve falls at twice the rate Mr=1-2X X The second graph shows the case of constant elasticity. The demand curve which has constant elasticity n is given MR=P(1-1/m) Denand and Supply Market Equilibrium Putting supply and demand together yields the familiar equilibrium diagram. The second graph shows a"perfectly inelastic"supply curve. the third graph shows a"perfectly elastic"one. Price is solely determined by demand in the first case and solely by supply in the second
Consumption — Demand and Supply 7 Marginal Revenue Curves • The first graph shows linear demand P = 1 − X. The marginal revenue curve falls at twice the rate MR = 1 − 2X. . ....................................................................................................................................... . ...................................................................................................................................... ................................................................................................................................................................................................................................................................................ . ................................................................................................................................................................................................................................................................................ 0 P X 0 P X P(X) MR P(X) MR • The second graph shows the case of constant elasticity. The demand curve which has constant elasticity η is given by X = aPη where a is a constant. So marginal revenue is MR = P(1 − 1/|η|). Consumption — Demand and Supply 8 Market Equilibrium • Putting supply and demand together yields the familiar equilibrium diagram. ................................................................................................................................................................................................................................................................................ .................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................. . . . . . .................................................................................................................................................................................................................................................... 0 P X 0 P X 0 P X D S D S D P S ∗ P ∗ P ∗ X∗ X∗ X∗ . . . . . . ............. ............. ............. ............. ............. ........... . . . . . . ............. ............. ............. ............. ............. ........... • The second graph shows a “perfectly inelastic” supply curve, the third graph shows a “perfectly elastic” one. • Price is solely determined by demand in the first case and solely by supply in the second
Consumption- Dead and supply Comparative Static A reduction in supply causes the supply to shift to the left. A reduction in demand causes the demand curve to shift to the left. This is illustrated in the below diagram. The equilibrium price and quantity change from Pl to P2 and X to X2 respective Denand and Supply Taxation When a tax is introduced the price the demander pays is not equal to the price the supplier gets. A quantity tax t means PD= Ps+t. The demander must pay the price the supplier sets plus the tax which is collected by the state. Alternatively, Ps= PD-t. the supplier gets the price the demander pays less the tax. An ad valorem tax t means PD= Ps(1+t). In both cases it is possible to shift either D or S to the left XxL The diagram shows a quantity tax. The vertical thick line is of length t, the tax paid The total tax revenue is tXa which is the area of the box between the thick vertical line and the ax
Consumption — Demand and Supply 9 Comparative Statics • A reduction in supply causes the supply curve to shift to the left. A reduction in demand causes the demand curve to shift to the left. This is illustrated in the below diagram. ................................................................................................................................................................................................................................................................................ . . . . 0 P X D1 S 1 D2 S 2 P 1 P 2 X2 X1 • • . . . . . . ............. ............. ............. ............. ......... . . . . . ............. ............. ............. ............. ............. ............. • The equilibrium price and quantity change from P 1 to P 2 and X1 to X2 respectively. Consumption — Demand and Supply 10 Taxation • When a tax is introduced the price the demander pays is not equal to the price the supplier gets. • A quantity tax t means PD = PS + t. The demander must pay the price the supplier sets plus the tax — which is collected by the state. Alternatively, PS = PD − t, the supplier gets the price the demander pays less the tax. • An ad valorem tax t means PD = PS(1 + t). In both cases it is possible to shift either D or S to the left. ...................................................................................................................................................................................................................................................................................................................................... . . . 0 P X D1 S 1 D2 S 2 P 1 P S P D X2 X1 • • • . . . . . . ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ........... ............. ............. ............. ............. ............. ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • The diagram shows a quantity tax. The vertical thick line is of length t, the tax paid. • The total tax revenue is tX2 which is the area of the box between the thick vertical line and the axis