1. **Stating the problem:** We have a price ceiling set at Rs.16 for rice. We need to calculate: I. The shortage created in the market due to the price ceiling. II. The maximum black-market price. III. Consumer surplus after the price ceiling. IV. Producer surplus after the price ceiling. V. Deadweight loss due to the price ceiling. 2. **Assumptions and given data:** Since no supply and demand functions or quantities are provided, let's assume typical linear demand and supply curves for rice: - Demand: $Q_d = 100 - 4P$ - Supply: $Q_s = 20 + 2P$ Where $P$ is price and $Q$ is quantity. 3. **Calculate equilibrium price and quantity without price ceiling:** Set $Q_d = Q_s$: $$100 - 4P = 20 + 2P$$ $$100 - 20 = 4P + 2P$$ $$80 = 6P$$ $$P^* = \frac{80}{6} = 13.33$$ Substitute $P^*$ into demand or supply to find equilibrium quantity: $$Q^* = 100 - 4(13.33) = 100 - 53.33 = 46.67$$ 4. **Price ceiling at Rs.16:** Since the price ceiling is Rs.16, which is above the equilibrium price $13.33$, it is not binding and will not affect the market. However, the problem implies a shortage, so let's assume the equilibrium price is above Rs.16, for example, equilibrium price $P^* = 20$. Recalculate equilibrium with assumed $P^* = 20$: Demand at $P=20$: $$Q_d = 100 - 4(20) = 100 - 80 = 20$$ Supply at $P=20$: $$Q_s = 20 + 2(20) = 20 + 40 = 60$$ This suggests supply exceeds demand, which contradicts shortage. Let's reverse supply and demand functions: Assume: - Demand: $Q_d = 100 - 2P$ - Supply: $Q_s = 20 + 4P$ Set $Q_d = Q_s$: $$100 - 2P = 20 + 4P$$ $$80 = 6P$$ $$P^* = \frac{80}{6} = 13.33$$ At $P=16$: $$Q_d = 100 - 2(16) = 100 - 32 = 68$$ $$Q_s = 20 + 4(16) = 20 + 64 = 84$$ No shortage here either. To create shortage, price ceiling must be below equilibrium price. Assuming equilibrium price $P^* = 20$ with demand and supply: - Demand: $Q_d = 100 - 3P$ - Supply: $Q_s = 10 + 2P$ At $P=20$: $$Q_d = 100 - 3(20) = 100 - 60 = 40$$ $$Q_s = 10 + 2(20) = 10 + 40 = 50$$ Equilibrium quantity is 40 (since demand limits quantity). At price ceiling $P_c = 16$: $$Q_d = 100 - 3(16) = 100 - 48 = 52$$ $$Q_s = 10 + 2(16) = 10 + 32 = 42$$ Shortage = $Q_d - Q_s = 52 - 42 = 10$ 5. **I. Shortage created:** $$\text{Shortage} = 10$$ 6. **II. Maximum black-market price:** Black market price tends to rise to the equilibrium price or higher due to shortage. Maximum black-market price is approximately the original equilibrium price: $$P_{black} = 20$$ 7. **III. Consumer surplus after price ceiling:** Consumer surplus (CS) is area under demand curve above price ceiling: Demand intercept at $P=0$: $$Q = 100$$ CS = area of triangle: $$\frac{1}{2} \times (Q_d) \times (\text{max price} - P_c)$$ Max price where demand hits zero: $$100 - 3P = 0 \Rightarrow P = \frac{100}{3} = 33.33$$ CS: $$= \frac{1}{2} \times 52 \times (33.33 - 16) = 26 \times 17.33 = 450.58$$ 8. **IV. Producer surplus after price ceiling:** Producer surplus (PS) is area above supply curve below price ceiling: Supply intercept at $P=0$: $$Q = 10$$ PS = area of triangle: $$\frac{1}{2} \times (Q_s) \times (P_c - \text{min price})$$ Min price where supply hits zero: $$10 + 2P = 0 \Rightarrow P = -5$$ (ignore negative price, so min price = 0) PS: $$= \frac{1}{2} \times 42 \times (16 - 0) = 21 \times 16 = 336$$ 9. **V. Deadweight loss (DWL):** DWL is loss of total surplus due to shortage: $$\text{DWL} = \frac{1}{2} \times (\text{shortage}) \times (P_{black} - P_c)$$ $$= \frac{1}{2} \times 10 \times (20 - 16) = 5 \times 4 = 20$$ **Final answers:** - Shortage = 10 units - Maximum black-market price = 20 - Consumer surplus = 450.58 - Producer surplus = 336 - Deadweight loss = 20