As explained in the chapter, economic efficiency is an outcome in a market when the marginal benefit to consumers of the last unit produced is equal to its marginal cost of production.
Considering this explanation of economic efficiency, why does a tax creates deadweight loss (i. e. reduce surplus)?
What is the impact of a production tax on the equilibrium price? The equilibrium price .

1) Taxes always create a deadweight loss because they lower total economic surplus (both consumer and supplier surplus). When a good is taxed, its selling price increases, therefore consumer surplus decreases. And even though the selling price increased, the revenue received by the supplier decreases. Since consume surplus and supplier decrease, the equilibrium quantity decreases, therefore resulting in a deadweight loss.

2) The impact of a production tax on the equilibrium price will be that it INCREASES and the equilibrium quantity decreases.

A tax increases the price a buyer pays for a product, so if the price is higher, then the quantity demanded will be lower.

It doesn´t matter if the tax is levied upon the supplier or the buyer, since the result will be the same, a higher price for the product. The buyer only cares for the total price he or she pays (including taxes) and the producer only cares about the net revenue they get from a sale (discounting taxes).

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u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30