1. **State the problem:** We are asked to recalculate the new equilibrium price and quantity in the cage-free egg market after an increase of 183.6 million dozen eggs (0.1836 billion dozens) is added to supply, given a price elasticity of supply $\varepsilon_s = 2$. We also need to find the change in social surplus. 2. **Known data from the problem:** - Initial equilibrium price $P_0 = 3.78$ - Initial quantity $Q_0 = 1.01$ billion dozens - New quantity after original increase $Q_1 = 1.13$ billion dozens (from the original elasticity 0.5 case) - Change in quantity $\Delta Q = 0.1836$ billion dozens - Original price elasticity of supply $\varepsilon_s = 0.5$ (for reference) - New price elasticity of supply $\varepsilon_s = 2$ 3. **Recall the price elasticity of supply formula:** $$\varepsilon_s = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}} = \frac{\frac{\Delta Q}{Q_0}}{\frac{\Delta P}{P_0}}$$ Rearranged to find price change: $$\frac{\Delta P}{P_0} = \frac{\frac{\Delta Q}{Q_0}}{\varepsilon_s}$$ 4. **Calculate the percentage change in quantity:** $$\frac{\Delta Q}{Q_0} = \frac{0.1836}{1.01} \approx 0.1817$$ 5. **Calculate the expected percentage change in price with new elasticity 2:** $$\frac{\Delta P}{P_0} = \frac{0.1817}{2} = 0.09085$$ Since an increase in supply shifts supply to the right, price falls, so $\Delta P$ is negative: $$\Delta P = -0.09085 \times P_0 = -0.09085 \times 3.78 \approx -0.343$$ 6. **Calculate the new equilibrium price:** $$P_1 = P_0 + \Delta P = 3.78 - 0.343 = 3.437$$ 7. **Calculate the new equilibrium quantity:** $$Q_1 = Q_0 + \Delta Q = 1.01 + 0.1836 = 1.1936$$ billion dozens 8. **Calculate the change in social surplus:** Social surplus change due to supply increase can be approximated as the area of the triangle between old and new supply curves (price and quantity changes): $$\Delta Surplus = \frac{1}{2} \times \Delta Q \times |\Delta P| = \frac{1}{2} \times 0.1836 \times 0.343 \approx 0.0315$$ (billion dollar-equivalents) 9. **Summary:** - New equilibrium price: $3.44$ dollars (approx) - New equilibrium quantity: $1.19$ billion dozens (approx) - Increase in social surplus: $0.0315$ (approx) billion dollars