What is the market demand and supply for a product, respectively, are: Q_d = 40 - 4P_x and Q_s = 3P_x - 9, where Q_d is quantity of the product demanded, Q_s is quantity of product supplied, and P_x is unit price of the product.

(a)What is the demand and supply equations above, clearly show your steps and derive the inverse demand and supply functions for the product (in fractions or at least 3 decimal points). Explain why the derived inverse supply function is legitimate.

(b)With the inverse demand and supply functions in (a), clearly show your steps and calculate the market equilibrium price and quantity for the product (in fractions or at least 3 decimal points).

(c)What if the government imposes a market price of $8.50 per unit on the product. Explain the economic rationale for such an action by the government. show an example of such an action in the United States.

(d)What If the government imposes a $5/unit excise tax on the product, clearly show your steps and calculate the new (after-tax) equilibrium price and quantity (in fractions or at least 3 decimal points).