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AP ECON 2300 F2012 Session 9.doc

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Department
Economics
Course
ECON 2300
Professor
Wai Ming Ho
Semester
Fall

Description
AP ECON 2300 F2012 Session 9 Instructor: Dr. David K. Lee Page 1 of19 Department of Economics York University Page 2of 19 Topic: Equilibrium and Technology Reading: Chapters 16 and 18 Ch 16: Equilibrium Market Equilibrium • A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. • D(p*) = S(p*); the market is in equilibrium. • D(p”) > S(p”); an excess of quantity demanded over quantity supplied Market price must rise towards p*. • D(p’) < S(p’); an excess of quantity supplied over quantity demanded. Market price must fall towards p*. • An example of calculating a market equilibrium when the market demand and supply curves are linear D( p) = a − bp S( p) = c + dp At the equilibrium price p*, D(p*) = S(p*). a − bp* = c + dp* p = a −c q = D(p ) = S(p ) = ad +bc . b + d b + d Market Equilibrium Market Market p demand supply S(p) = c+dp D(p) = a-bp D(p), S(p) © 2010 W. W. Norton & Company, Inc. 19 Can we calculate the market equilibrium using the inverse market demand and supply curves? Yes, it is the same calculation. q = D(p) = a −bp ⇔ p = a − q= D (q), q = S(p) = c + dp ⇔ p = −c + q = S (q), b d -1 -1 At the equilibrium quantity q*, D (p*) = S (p*). Page 3 of 19 * * ad +bc a − c a − q = − c + q q = p = D (q ) = S (q ) = . b d b + d b + d Market Equilibrium D (q), Market Market S (q) demand supply S (q) = (-c+q)/d -1 D (q) = (a-q)/b q © 2010 W. W. Norton & Company, Inc. 29 Two special cases: – quantity supplied is fixed, independent of the market price, and – quantity supplied is extremely sensitive to the market price Market Equilibrium p Market Market quantity supplied is demand fixed, independent of price. S(p) = c+dp, so d=0 and S(p) ≡ c. -1 p* = p* = D (q*); that is, (a-c)/b p = (a -c)/b. D (q) = (a -q)/b q* = c q with d = 0 give © 2010 W. W. Norton & Company, Inc. 37 Page 4 of19 Market Equilibrium p Market Market quantity supplied is demand extremely sensitive to price. S (q) = p*. p* = D (q*) = (a-q*)/b so p* q* = a-bp* D (q) = (a-q)/b q* = q a-bp* © 2010 W. W. Norton & Company, Inc. 43 Quantity Taxes • A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded. • If the tax is levied on sellers then it is an excise tax. • If the tax is levied on buyers then it is a sales tax. • What is the effect of a quantity tax on a market’s equilibrium? • How are prices affected? • How is the quantity traded affected? • Who pays the tax? • How are gains-to-trade altered? A tax rate t makes the price paid by buyersb p , higher by t from the price received by ssllers, p . p − p = t b s Quantity Taxes & Market Market EquilibMarket p demand supply An excise tax raises the market p b $t supply curve by $t, p* raises the buyers’ p s price and lowers the quantity traded. q t q* D(p), S(p) And sellers receive only p s = p b- t. © 2010 W. W. Norton & Company, Inc. 53 Page 5 of19 Quantity Taxes & Market Equilibrium p Market Market demand supply An sales tax lowers the market demand p b curve by $t, lowers p* the sellers’ price and p s reduces the quantity $t traded. t q q* D(p), S(p) And buyers pay p b = p s + t. © 2010 W. W. Norton & Company, Inc. 57 Who pays the tax of $t per unit traded? The division of the $t between buyers and sellers is the incidence of the tax. Tax Incidence and Own-Price Elasticities Change to buyers’ price is b - p*. Change to quantity demanded is Δ q. Around p = p* the own-price elasticity of demand is approximately Δq q* Δq × p* ε D *⇒ p b p ≈* * . pb− p εD× q * p Tax Incidence and Own -Price Market ElastiMarket p demand supply Tax paid by buyers p b p* Tax paid by p s sellers qt q* D(p), S(p) Tax incidence = © 2010 W. W. Norton & Company, Inc. 84 p − p * Tax incidence = b . p − p s Page 6 of19 * * * p − p ≈ Δq × p .p − p ≈ Δq× p .  p b p ε S b εD× q* s ε ×q * p − p ≈− ε . S s D • The fraction of a $t quantity tax paid by buyers rises as supply becomes more own-price elastic or as demand becomes less own-price elastic. Deadweight Loss and Own-Price Elasticities Deadweight Loss and Own -Price Market Elasticities p Market demand supply Deadweight loss falls pb $t as market demand p* becomes less own - ps price elastic. q q* D(p), S(p) © 2010 W. W. Norton & Company, Inc. 107 Tax Incidence and Own -Price Elasticities p Market Market demand supply As market demand p $t becomes less own - b price elastic, tax p s p* incidence shifts more to the buyers. t q = q* D(p), S(p) When ε = 0, buyers pay the entire tax, even D though it is levied on the sellers. © 2010 W. W. Norton & Company, Inc. 91 • Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic. • If eitherDe = 0 oS e = 0 then the deadweight loss is zero. Ch 18 Technology Technologies Page 7 of 19 • A technology is a process by which inputs are converted to an output. • E.g. labor, a computer, a projector, electricity, and software are being combined to produce this lecture. • Usually several technologies will produce the same product -- a blackboard and chalk can be used instead of a computer and a projector. • Which technology is “best”? • How do we compare technologies? Input Bundles • x denotes the amount used of input i; i.e. the level of input i. i • An input bundle is a vector of the input levels; (x1, x2, … , xn). • E.g. (x1, x2, 3 ) = (6, 0, 9×3). Production Functions • y denotes the output level. • The technology’s production function states the maximum amount of output possible from an input bundle. y = f (x , , x ) 1 n Production Functions One input, one output Output Level y = f(x) is the production function. y’ y’ = f(x’) is the maximal output level obtainable from x’ input units. x’ x © 2010 W. W. Norton & Company, Inc. Level 6 Technology Sets • A production plan is an input bundle and an output level; (x , … , x1, y). n • A production plan is feasible if y ≤ f (x 1 , x n • The collection of all feasible production plans is the technology set. Technology Sets One input, one output Output Level y = f(x) is the production y’ function. y’ = f(x’) is the maximal output level obtainable from x’ input units. y” y” = f(x’) is an output level that is feasible from x’ input units. x’ x Input Level © 2010 W. W. Norton & Company, Inc. 8 The technology set is Page 8 of 19 T={( x1 ,xny)|y≤f(x, 1 ,xnand x ≥0 , ,x ≥0 }. 1 n Technology Sets One input, one output Output Level Technically y’ efficient plans The technology y” Technically set inefficient plans x’ x Input Level © 2010 W. W. Norton & Company, Inc. 11 Technologies with Multiple Inputs • What does a technology look like when there is more than one input? • The two input case: Input levels are x a1d x . O2tput level is y. • Suppose the production function is 1/3 1/3 y = f (x1, 2 ) = 2x1 x 2 . • E.g. the maximal output level possible from the input bundle (x , 1 ) 2 (1, 8) is 1/3 1/3 1/3 1/3 y = 2x 1 x 2 = 2×1 ×8 = 2×1× 2 = 4. • And the maximal output level possible from (x ,x1) 2 (8,8) is y = 2x11/x 2/3= 2×8 ×8/3 1/3 = 2× 2× 2 = 8. • The y output unit isoquant is the set of all input bundles that yield at most the same output level y. Isoquants with Two Variable x2 Inputs y ≡8 y ≡6 y ≡2 x 1 © 2010 W. W. Norton & Company, Inc. 20 Page 9 of19 • The complete collection of isoquants is the isoquant map. • The isoquant map is equivalent to the production function -- each is the other. • E.g. 1/3 1/3 y = f (x 1 x2) = 2x 1 x 2 Cobb-Douglas Technologies a y = Ax 1a1 22 ××x . nn Example: 1 1 y = x1/3x2/3 n = 2,A = 1,a 1 and a 2 .
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