blanchard_ch03

Qxd 62209 856 am page 75 mathematical note market

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Unformatted text preview: curve and the supply curve. We can use the equations to find the equilibrium price and equilibrium quantity. The price of a good adjusts until the quantity demanded Q D equals the quantity supplied Q S. So at the equilibrium price (P* ) and equilibrium quantity (Q* ), P* = a - b a P* = a-c b b+d a1b + d2 - b1a - c2 b+d ad + bc P* = . b+d Alternatively, using the supply equation, we have Q D = Q S = Q *. P* = c + d a To find the equilibrium price and equilibrium quantity, substitute Q* for QD in the demand equation and Q* for QS in the supply equation. Then the price is the equilibrium price (P*), which gives P* = a-c b b+d c1b + d2 + d1a - c2 b+d ad + bc P* = . b+d P * = a - bQ * P * = c + dQ *. An Example Notice that a - bQ * = c + dQ *. The demand for ice-cream cones is Now solve for Q *: P = 800 - 2Q D. a - c = bQ * + dQ * a - c = 1b + d2Q * a-c Q* = . b+d To find the equilibrium price, (P* ), substitute for Q* in either the demand equation or the supply equation. The supply of ice-cream cones is P = 200 + 1Q S. The price of a cone is expressed in cents, and the quantities are expressed in cones per day. To find the equilibrium price (P *) and equilibrium quantity (Q *), substitute Q * for Q D and Q S and P * for P. That is, Price P * = 800 - 2Q * P * = 200 + 1Q *. Supply Market equilibrium Now solve for Q *: 800 - 2Q * = 200 + 1Q * 600 = 3Q * P* Q * = 200. And Demand 0 Q* Quantity Figure 3 Market equilibrium P * = 800 - 212002 = 400. The equilibrium price is $4 a cone, and the equilibrium quantity is 200 cones per day. 9160335_CH03_p053-080.qxd 76 6/22/09 8:56 AM Page 76 CHAPTER 3 Demand and Supply SUMMARY ◆ Key Points ■ Markets and Prices (p. 54) ■ ■ ■ A competitive market is one that has so many buyers and sellers that no single buyer or seller can influence the price. Opportunity cost is a relative price. Demand and supply determine relative prices. Market Equilibrium (pp. 64–65) ■ ■ Demand (pp. 55–59) ■ ■ ■ Demand is the relationship between the quantity demanded of a good and its price when all other influences on buying plans remain the...
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