Question

the following table presents the weekly demand and supply in the market for wireless earbuds in detroit.
price (dollars per pair of wireless earbuds) quantity demanded (pairs of wireless earbuds) quantity supplied (pairs of wireless earbuds)
12 2,200 400
24 1,800 800
36 1,600 1,000
48 1,200 1,800
60 1,000 2,400

on the following graph, plot the demand for wireless earbuds using the blue point (circle symbol). next, plot the supply of wireless earbuds using the orange point (square symbol). finally, use the black point (plus symbol) to indicate the equilibrium price and quantity in the market for wireless earbuds.
note: plot your points in the order in which you would like them connected. line segments will connect the points automatically.

Explanation:

Step1: Identify demand data points

The demand points are: $(2200, 12)$, $(1800, 24)$, $(1600, 36)$, $(1200, 48)$, $(1000, 60)$

Step2: Identify supply data points

The supply points are: $(400, 12)$, $(800, 24)$, $(1000, 36)$, $(1800, 48)$, $(2400, 60)$

Step3: Find equilibrium point

Equilibrium occurs where quantity demanded = quantity supplied. Check each price:

• At $P=36$, $Q_d=1600$, $Q_s=1000$ (not equal)
• At $P=48$, $Q_d=1200$, $Q_s=1800$ (not equal)
• Interpolate: Set $Q_d=Q_s$.

Demand function: Let $Q_d = a - bP$. Using $(2200,12)$ and $(1000,60)$:
Slope $b=\frac{2200-1000}{12-60}=-\frac{1200}{48}=-25$, so $Q_d=2200-25(P-12)=2500-25P$
Supply function: Let $Q_s = c + dP$. Using $(400,12)$ and $(2400,60)$:
Slope $d=\frac{2400-400}{60-12}=\frac{2000}{48}=\frac{125}{3}$, so $Q_s=400+\frac{125}{3}(P-12)=\frac{125}{3}P$
Set $2500-25P=\frac{125}{3}P$
$2500=\frac{125}{3}P + 25P=\frac{125P+75P}{3}=\frac{200P}{3}$
$P=\frac{2500\times3}{200}=37.5$
$Q=\frac{125}{3}\times37.5=1562.5$
Alternatively, the closest matching point where $Q_d$ and $Q_s$ converge is between $P=36$ and $P=48$, with equilibrium at $(1500, 40)$ (simplified market equilibrium approximation from the table's trend, or precise calculation gives $(1562.5, 37.5)$)

Answer:

1. Demand curve points (to plot with blue circles):

• (2200, 12), (1800, 24), (1600, 36), (1200, 48), (1000, 60)

1. Supply curve points (to plot with orange squares):

• (400, 12), (800, 24), (1000, 36), (1800, 48), (2400, 60)

1. Equilibrium point (to plot with black plus):

Precise: $(1562.5, 37.5)$; approximate market equilibrium from table trend: $(1500, 40)$