The inverse demand P(Q) for bowling balls is given by P = 100 - 5Q where P is the price of bowling balls and Q is the consumption of bowling balls. One store sells bowling balls, the supply is given by P = 50 + 5Q.

a) What is the total quantity of bowling balls consumed and what is the price per unit. What is the consumer surplus and the producer surplus.

b) The government set a tax of $10 on bowling balls, what is the total quantity of bowling balls consumed, the price paid by consumer and the price received by the store. What is the consumer surplus, the producer surplus, the tax revenue and the deadweight loss. What is the share of the tax paid by the consumer and the one paid by the producer.