Here are notes on the solution. As with some of the other solution sheets, most of the algebra is omitted and the explanations are a bit terse. If you have any questions, please don't hesitate to stop by during office hours or the lab session to talk over things in detail.
Removing the quota would cause the market supply curve to be flat once the foreign producers enter at $0.12. The new market diagram looks as follows:
The result is a 50% drop in the price. The quantities were found using the demand and supply elasticities. Using the price change and the supply elasticity for the US gives the change in US production: 1.5*(-50%) = -75%. US output thus drops to 0.25*14 = 3.5 billion pounds. Using the price change and the demand elasticity to find the change in the quantity consumed: (-0.3)*(-50%) = 15% increase. Consumption thus rises to 1.15*18 = 20.7 billion pounds. The quantity imported is the difference: 20.7 - 3.5 = 17.2 billion pounds.
The change in CS is D+E:
The change in PS for US producers is A:
The change in PS for the importers is C:
The problem does not ask you to report the values of the areas but in case you calculated them anyway to prepare for the next question, they are as follows (rounded to the nearest $10 million): A = $1.05 billion; C = $480 million; D = $160 million; and E = $2.16 B.
Magnitudes are large in absolute value (billions of dollars, not merely millions). Effect on the industry is dramatic: the transfer to producers ($1.05 billion) is about a third of the entire revenue of the US sugar industry ($0.24 times 14 billion); the lost CS nearly doubles the cost of sugar to consumers. Gain in CS is more than twice loss of PS. Policy is highly inefficient: a different policy that transferred $1.05 billion directly from consumers to producers would leave producers just as well off but would save consumers $1.27 billion.
Effect on politics is a bit subtle: the policy raises costs to consumers but no individual spends much on sugar; only a small number of firms produce sugar and the policy increases profits substantially. Would expect that sugar producers would lobby much harder to preserve the limits than consumers would lobby to remove them. The policy is probably one of the reasons for the widespread use of corn syrup in soft drinks, by the way.