15. Equilibrium

15. Equilibrium - Equilibrium Professor John Diamond ECON...

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Unformatted text preview: Equilibrium Professor John Diamond ECON 370: Microeconomic Theory Lecture 15 2 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q* D(p*) = S(p*); market is in equilibrium 3 p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* S(p) D(p) < S(p); Market price must fall towards p* p D(p) Market Equilibrium: p>p*, Excess Supply 4 p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* D(p) D(p) > S(p); Market price must rise towards p* p S(p) Market Equilibrium: p<p*, Excess Demand 5 Market Equilibrium: Linear Curves Example: Market equilibrium when demand and supply curves are linear bp a ) p ( D dp c ) p ( S 6 p D(p), S(p) D(p) = a-bp S(p) = c+dp p* q* How to calculate values of p* and q*? Market Equilibrium: Graph Mkt D Mkt S 7 Market Equilibrium: Equations bp a ) p ( D dp c ) p ( S At equilibrium price p*, D(p*) = S(p*) a - bp* = c + dp* p* = a c b + d q * = D(p*) = S(p*) = ad + bc b + d 8 p D(p), S(p) D(p) = a-bp S(p) = c+dp d b c a p * d b bc ad q * Market Equilibrium: Graph Mkt D Mkt S 9 Market Equilibrium: Inverse Curves ) q ( D b q a p bp a ) p ( D q 1 ) q ( S d q c p dp c ) p ( S q 1 Equation of inverse market demand curve Equation of the inverse market supply curve 10 q D-1 (q), S-1 (q) D-1 (q) = (a-q)/b Market inverse demand S-1 (q) = (-c+q)/d p* q* At equilibrium, D-1 (q*) = S-1 (q*) Market inverse supply Market Equilibrium: Graph 11 Market Equilibrium: Inverse Equations b q a ) q ( D p 1 d q c ) q ( S p 1 and At equilibrium quantity q*, D-1 (p*) = S-1 (p*). d q c b q a * * d b bc ad q * d b c a ) q ( S ) q ( D p * 1 * 1 * 12 q D-1 (q), S-1 (q) D-1(q) = (a-q)/b S-1 (q) = (-c+q)/d p a c b d * d b bc ad q * Market Equilibrium: Graph Mkt D Mkt S 13 Market Equilibrium: Special Cases Two special cases: Case 1: Perfectly inelastic supply quantity supplied is fixed, independent of market price Case 2: Perfectly elastic supply quantity supplied is extremely sensitive to price 14 p q q* = c Equilibrium Perfectly Inelastic Supply Mkt qty supplied is fixed, independent of price S(p) = c+dp, so d=0 and S(p) c 15 p q p* D-1 (q) = (a-q)/b Market demand q* = c Equilibrium Perfectly Inelastic Supply S(p) = c+dp, so d=0 and S(p) c 16 p q p* = (a-c)/b D-1(q) = (a-q)/b...
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15. Equilibrium - Equilibrium Professor John Diamond ECON...

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