Supply Demand
1. The problem gives a table of prices with the corresponding quantities demanded (Qd) and quantities supplied (Qs).
2. We want to analyze the supply and demand relationship from the data provided.
3. Notice the price points: $120, $150, $180, $210, $240.
4. Look for the price where quantity demanded equals quantity supplied.
5. From the table, Qd = Qs at price $150, with both Qd and Qs equal to 40.
6. This price is the market equilibrium price where supply and demand balance.
7. To express demand and supply as linear functions, we can use two points from each to find slopes and intercepts.
8. For Demand, using points (120,50) and (240,24):
Calculate slope $m_d = \frac{24 - 50}{240 - 120} = \frac{-26}{120} = -\frac{13}{60}$.
Use point-slope form to find intercept $b_d$: $50 = -\frac{13}{60} \times 120 + b_d$ thus $b_d = 50 + 26 = 76$.
Demand function: $Q_d = -\frac{13}{60} P + 76$.
9. For Supply, using points (120,36) and (240,70):
Calculate slope $m_s = \frac{70 - 36}{240 - 120} = \frac{34}{120} = \frac{17}{60}$.
Use point-slope form to find intercept $b_s$: $36 = \frac{17}{60} \times 120 + b_s$ thus $b_s = 36 - 34 = 2$.
Supply function: $Q_s = \frac{17}{60} P + 2$.
10. Graphs of these functions would intersect at the equilibrium point (P=150, Q=40).
Final answer: Equilibrium price is $150$ with quantity $40$.
Demand: $Q_d = -\frac{13}{60} P + 76$.
Supply: $Q_s = \frac{17}{60} P + 2$.