The government in the nation of Taxico has chosen to create a new national park. Tax revenues must be collected in order to cover the costs of the new park. In order to generate tax revenue, the government plans to implement taxes on onions and carrots. The markets for onions and carrots are free from externalities and any other such complications; accordingly, the First Fundamental Theorem of Welfare Economics applies perfectly well to these vegetable markets.
The onion market in Taxico is characterized by the following aggregate supply and demand functions (in which onion quantities are measured in units of tons):
S(pS) = 3pS − 500
D(pD) = 10, 000 − 2pD.
The carrot market in Taxico is characterized by the following aggregate supply and demand functions (in which carrot quantities are measured in units of tons):
S(pS) = 2pS − 5000
D(pD) = 10, 000 − pD
You are the head supervisor to the prime minister of Taxico, who has proposed that the park be funded through “Tax Plan A,” which involves a tax of $1800 per ton of onions alongside a tax of $1800 per ton of carrots. Both taxes will be collected from vegetable producers. (a) Altogether, how many dollars of tax revenue will be generated by Tax Plan A?

Great news: It turns out that Tax Plan A will generate exactly enough tax revenue
to cover the cost of the new park. But apple producers have learned about the plan,
and they’re upset. Their lobbyist presents you with an alternative plan, “Tax Plan
B,” which involves a tax of $1200 per ton of onions alongside a tax of $2400 per ton
of carrots. The lobbyist claims that Tax Plan B would generate exactly as many
dollars of tax revenue as would Tax Plan A, and they encourage you to implement
Plan B instead.
(b) Demonstrate whether the lobbyist’s claim is accurate. How much tax revenue
would be generated by Tax Plan B?

(c) Between Tax Plans A and B, which plan is preferable in terms of overall social
welfare?