Consider the demand equation: P=10-Q and supply equation: P=Q

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Consider the demand equation: P=10-Q and supply equation: P=Q.

a. Calculate the equilibrium price and quantity.

b. Calculate the consumer surplus, producer surplus, and total surplus at equilibrium.

c. Suppose the government imposes a tax of $2 for each unit bought. Derive the new equilibrium price that consumers pay, the price that firms receive, and quantity.

d. Calculate the deadweight loss of this tax.

e. In a diagram, show the equilibrium in part a and the equilibrium in part c; and the areas that you computed in part b and d.