Suppose 70 is the equilibrium price in the bicycle market.The equilibrium quantity is 32 bicycles. If the price equals 55 there is no market supply. Determine producer surplus Enter the exact value Do not round.

To calculate the **producer surplus**, we need to understand the concept. Producer surplus is the area above the supply curve and below the equilibrium price in a market. It represents the difference between what producers are willing to accept for a good (as indicated by the supply curve) and what they actually receive (the market price).<br /><br />### Given:<br />- Equilibrium price (\(P_e\)) = \$70<br />- Equilibrium quantity (\(Q_e\)) = 32 bicycles<br />- At \(P = \$55\), there is no market supply (\(Q = 0\)).<br /><br />This implies that the supply curve starts at \((P = 55, Q = 0)\) and rises linearly to \((P = 70, Q = 32)\). The producer surplus is the area of the triangle formed under the equilibrium price and above the supply curve.<br /><br />---<br /><br />### Step 1: Find the slope of the supply curve<br />The supply curve is linear, so we can calculate its slope using the two points:<br />\[<br />(P_1, Q_1) = (55, 0) \quad \text{and} \quad (P_2, Q_2) = (70, 32).<br />\]<br />The slope (\(m\)) of the supply curve is:<br />\[<br />m = \frac{\Delta P}{\Delta Q} = \frac{70 - 55}{32 - 0} = \frac{15}{32}.<br />\]<br /><br />Thus, the equation of the supply curve is:<br />\[<br />P = \frac{15}{32}Q + 55.<br />\]<br /><br />---<br /><br />### Step 2: Calculate producer surplus<br />Producer surplus is the area of the triangle under the equilibrium price (\$70) and above the supply curve, from \(Q = 0\) to \(Q = 32\). The height of the triangle is:<br />\[<br />\text{Height} = 70 - 55 = 15.<br />\]<br />The base of the triangle is:<br />\[<br />\text{Base} = Q_e = 32.<br />\]<br />The area of the triangle (producer surplus) is:<br />\[<br />\text{Producer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height}.<br />\]<br />Substitute the values:<br />\[<br />\text{Producer Surplus} = \frac{1}{2} \times 32 \times 15 = 240.<br />\]<br /><br />---<br /><br />### Final Answer:<br />The **producer surplus** is:<br />\[<br />\boxed{240}<br />\]