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.
- For case 1 (when the quota is in place), the supply by foreign sellers will 0 below $0.12, be horizontal at $0.12 up to 4B pounds, and then be vertical at 4B at all prices above $0.12. Graphing it:
The supply by US producers will look as shown below. The quantity for P=$0.12 is included because it's useful when combining the two supply curves to get the market supply. It can be found by using the US supply elasticity to calculate the impact of a 50% reduction in the price of sugar. The result would be a 75% reduction in output (a drop of 10.5B pounds) to a new output of 3.5B pounds.
Combining the two supply curves gives the overall market supply for case 1:
The market supply curve for case 2 (without the quota) is simpler. Since the foreign supply is perfectly elastic at $0.12, it looks like this:
- The overall market diagram for case 1 looks like this:
The market equilibrium is at P=$0.24 and Q=18B pounds, as given in the problem. For case 2, the diagram looks like this:
The equilibrium is at P=$0.12, a 50% drop relative to case 1. The new market Q can be calculated using the demand elasticity and the 50% decline in P. The result is a 15% increase (2.7B pounds) to a total of 20.7B pounds. Domestic production falls to 3.5B pounds and the quantity imported is the difference: 20.7B - 3.5B = 17.2B pounds.
- Changes in surplus are calculated using subsequent diagrams for each agent.The change in CS is a gain of D+E:
Calculating the areas: D = $160 million; and E = $2.16 billion. Thus, the total gain in CS is $2.32 billion. The change in PS for US producers is a loss of A:
Calculating the area gives A = $1.05 billion. The change in PS for foreign suppliers is a loss of C in the diagram below:
Calculating it gives C = $480 million, so foreign suppliers allowed to import under the quota would lose $480 million if it were removed.
The magnitudes are large in absolute value: billions or hundreds of millions of dollars. The effect of the quota 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 policy doubles the cost of sugar to consumers; and the loss of CS is more than twice the PS it delivers to producers. Overall, the 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.
- DWL: $790 million.The question doesn't ask for details but $630 million arises from the 10.5B pounds being produced in the US at higher cost than world markets (area B below) and $160 million is the foregone CS on the difference between 18B and 20.7B pounds of sugar (area D above).
- The 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. One 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.
- Jobs saved: 12,000; lost CS from above: $2.32 billion; lost CS per job saved: $193,500.
- This policy is very expensive for what it accomplishes. The loss to US consumers above and beyond the $1.05 billion transferred to US producers is $1.27 billion: $790 million in DWL plus $480 million to exporters with licenses. The cost per job saved is enormous: US farm workers typically earn $40k a year or less, so in effect the policy is costing $193k for each $40k job saved, and that excess cost occurs every year. The 12,000 farm workers whose jobs are protected would almost certainly would prefer a policy in which they'd leave the industry in exchange for a pension of much less than $193k. For example, if the pension paid $50,000, it would cost $600 million rather than $2.32 billion.
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Peter J Wilcoxen, The Maxwell School, Syracuse University