1. Problem 4a: Find equilibrium price and quantity where quantity demanded equals quantity supplied. Demand and supply data: Price: $4,5,6,7,8,9 Quantity Demanded: 135,104,81,68,53,39 Quantity Supplied: 26,53,81,98,110,121 At price $6, Qd=81 and Qs=81, so equilibrium price = 6 and equilibrium quantity = 81. 2. Problem 4b: If actual price is above equilibrium price (e.g., $7), quantity supplied > quantity demanded (Qs=98, Qd=68). This surplus causes sellers to reduce price towards equilibrium. 3. Problem 4c: If actual price is below equilibrium (e.g., $5), quantity demanded > quantity supplied (Qd=104, Qs=53). This shortage causes price to rise towards equilibrium. 4. Problem 5a: Demand and supply schedules for basketball tickets given. Supply quantity is constant (8000) regardless of price, which is unusual. This could be due to fixed stadium capacity. 5. Problem 5b: Equilibrium where Qd = Qs. At price $8, Qd=8000, Qs=8000, so equilibrium price = 8, quantity = 8000. 6. Problem 5c: New demand is sum of old and additional demand: At each price: $4: 10000 + 4000 = 14000 $8: 8000 + 3000 = 11000 $12: 6000 + 2000 = 8000 $16: 4000 + 1000 = 5000 $20: 2000 + 0 = 2000 Equilibrium occurs where new demand = supply = 8000, so at price $12, quantity = 8000. 7. Problem 6a: Market 1 equations: $supply: Qs = -20 + 3P$ $demand: Qd = 220 - 5P$ Set $Qs = Qd$ $$-20 + 3P = 220 - 5P$$ $$3P + 5P = 220 + 20$$ $$8P = 240$$ $$P = 30$$ Quantity: $$Qs = -20 + 3\times30 = -20 + 90 = 70$$ Equilibrium price = 30, quantity = 70. 8. Problem 6b: Given: $Qd - 128 + 9P = 0 \Rightarrow Qd = 128 - 9P$ $Qs + 32 - 7P = 0 \Rightarrow Qs = 7P - 32$ Set $Qd = Qs$ $$128 - 9P = 7P - 32$$ $$128 + 32 = 7P + 9P$$ $$160 = 16P$$ $$P = 10$$ Quantity: $$Q = 128 - 9\times10 = 128 - 90 = 38$$ Equilibrium price = 10, quantity = 38. 9. Problem 7a: Given: $$QS = 10P_{bj} - 5P_B$$ $$QD = 100 - 15P_{bj} + 10P_c$$ Fix $P_B = 1$, $P_c = 5$ Set $QS = QD$ $$10P_{bj} - 5 \times 1 = 100 - 15P_{bj} + 10 \times 5$$ $$10P_{bj} - 5 = 100 - 15P_{bj} + 50$$ $$10P_{bj} - 5 = 150 - 15P_{bj}$$ $$10P_{bj} + 15P_{bj} = 150 + 5$$ $$25P_{bj} = 155$$ $$P_{bj} = 6.2$$ Quantity: $$Q = 10\times6.2 - 5 = 62 - 5 = 57$$ Equilibrium price = 6.2, quantity = 57. 10. Problem 7b: Increase $P_B$ to 2 $$QS = 10P_{bj} - 5 \times 2 = 10P_{bj} - 10$$ Set supply = demand: $$10P_{bj} - 10 = 100 - 15P_{bj} + 50$$ $$10P_{bj} - 10 = 150 - 15P_{bj}$$ $$10P_{bj} + 15P_{bj} = 150 + 10$$ $$25P_{bj} = 160$$ $$P_{bj} = 6.4$$ Quantity: $$Q = 10\times6.4 - 10 = 64 - 10 = 54$$ New equilibrium price = 6.4, quantity = 54. 11. Problem 7c: $P_B=1$, $P_c=3$ $$QS = 10P_{bj} - 5$$ $$QD = 100 - 15P_{bj} + 30$$ Set equal: $$10P_{bj} - 5 = 130 - 15P_{bj}$$ $$10P_{bj} + 15P_{bj} = 130 + 5$$ $$25P_{bj} = 135$$ $$P_{bj} = 5.4$$ Quantity: $$Q = 10 \times 5.4 - 5 = 54 - 5 = 49$$ Equilibrium price = 5.4, quantity = 49. 12. Problem 7d: With price ceiling $P^* = 5$, quantity demanded and supplied are: Supply: $$Q_s = 10 \times 5 - 5 = 50 - 5 = 45$$ Demand: $$Q_d = 100 - 15 \times 5 + 50 = 100 - 75 + 50 = 75$$ Excess demand = $Q_d - Q_s = 75 - 45 = 30$ 13. Problem 8a: Calculate price elasticity of demand $E_p = \frac{\Delta Q / Q_{avg}}{\Delta P / P_{avg}}$ From price $7 \to 8$ and income $25000$: $$\Delta Q = 2800 - 2000 = -800$$ $$Q_{avg} = \frac{2800 + 2000}{2} = 2400$$ $$\Delta P = 8 - 7 = 1$$ $$P_{avg} = \frac{7 + 8}{2} = 7.5$$ $$E_p = \frac{-800 / 2400}{1 / 7.5} = \frac{-0.3333}{0.1333} = -2.5$$ For income $35000$: $$\Delta Q = 4600 - 3400 = -1200$$ $$Q_{avg} = 4000$$ $$E_p = \frac{-1200 / 4000}{1 / 7.5} = \frac{-0.3}{0.1333} = -2.25$$ 14. Problem 8b: Income elasticity $E_I = \frac{\Delta Q/Q_{avg}}{\Delta I/I_{avg}}$ At price 6: $$\Delta Q = 5400 - 3400 = 2000$$ $$Q_{avg} = 4400$$ $$\Delta I = 35000 - 25000 = 10000$$ $$I_{avg} = 30000$$ $$E_I = \frac{2000/4400}{10000/30000} = \frac{0.4545}{0.3333} = 1.36$$ At price 9: $$\Delta Q = 2200 - 1200 = 1000$$ $$Q_{avg} = 1700$$ $$E_I = \frac{1000/1700}{10000/30000} = \frac{0.5882}{0.3333} = 1.76$$