Question 19 8 pts Suppose demand is given by \( P=24-Q \) and supply is given by \( P=3+(0.5) Q \). The government imposes a price ceiling of \( \$ 8 \) in this market. At the original equilibrium (before implementing the price ceiling), what was the value of economic surplus? \( \square \) After the price celiing is implemented, what is the value of consumer surplus? (Just type the number; do not include a dollar sizn.) \( \square \) After the price celling is implemented, what is the size of the deadweight loss? (Just type the number; do not include a dollar sign.) \( \square \) After the price celing is implemented, what is the size of the shortage in the market? (Just type the number; do not include any text or units.) \( \square \)

We are given the demand and supply functions   Demand: P = 24 – Q   Supply: P = 3 + 0.5 Q and a government‐imposed price ceiling of $8. Step 1. Find the Original (Free‐Market) Equilibrium. Set demand equal to supply:   24 – Q = 3 + 0.5 Q   24 – 3 = Q + 0.5 Q  → 21 = 1.5 Q   Q* = 14. Substitute Q* = 14 into the demand equation:   P* = 24 – 14 = 10. Thus, free-market equilibrium is Q = 14 and P = 10. Step 2. Compute the Original Total (Economic) Surplus. • Consumer Surplus (CS) is the area of a triangle with height [maximum willingness to pay (24) – equilibrium price (10)] and base Q = 14:   CS = ½ × 14 × (24 – 10) = ½ × 14 × 14 = 98. • Producer Surplus (PS) is the area of a triangle with base Q = 14 and height [equilibrium price (10) – minimum price (the supply price at Q = 0, which is 3)]:   PS = ½ × 14 × (10 – 3) = ½ × 14 × 7 = 49. Thus, the original total economic surplus is   Total Surplus = CS + PS = 98 + 49 = 147. Answer for first box: 147 Step 3. Effects of the Price Ceiling at $8. Since the free‐market price (10) is above the ceiling (8), the price becomes fixed at $8. At P = 8: • Quantity demanded from the demand function:   Q_d = 24 – 8 = 16. • Quantity supplied from the supply function:   8 = 3 + 0.5 Q_s  → 0.5Q_s = 5  → Q_s = 10. Because less is supplied than demanded, a shortage occurs. Step 4. Compute Consumer Surplus after the Price Ceiling. Even though only 10 units are sold, the consumers who get the product are assumed to be the ones with the highest willingness to pay. Their surplus is found by integrating the difference between the demand price and the market price over the quantity transacted:   Consumer Surplus = ∫₀¹⁰ [(24 – Q) – 8] dQ     = ∫₀¹⁰ (16 – Q) dQ     = [16Q – 0.5 Q²] evaluated from 0 to 10     = (16×10 – 0.5×10²) – 0     = (160 – 50) = 110. Answer for second box: 110 Step 5. Compute the Deadweight Loss (DWL). Under the price ceiling, the total surplus is reduced due to the loss of mutually beneficial trades between Q = 10 and the free‐market Q = 14. The deadweight loss is given by the area of a triangle with:   Base = 14 – 10 = 4,   Height = difference between the demand and supply prices at Q = 10. At Q = 10:   Demand price = 24 – 10 = 14,   Supply price = 3 + 0.5×10 = 8.   Height = 14 – 8 = 6. Thus,   DWL = ½ × 4 × 6 = 12. Answer for third box: 12 Step 6. Find the Size of the Shortage. The shortage is the difference between the quantity demanded and supplied at the ceiling price.   Shortage = Q_d – Q_s = 16 – 10 = 6. Answer for fourth box: 6 Summary of Answers: 1. Original economic surplus: 147 2. Consumer surplus after the ceiling: 110 3. Deadweight loss after the ceiling: 12 4. Shortage in the market after the ceiling: 6