equilibrium price

Question
Suppose the market for natural gas can be described by:
Demand: Q^D = 100 ? 5P
Supply: Q^S = 20 + 15P

Where P is the price ($) of natural gas per million BTU, QD is quantity demanded and QS is quantity supplied of million BTUs of natural gas per day.

A. What is the equilibrium price P* and equilibrium quantity Q*?
B. Suppose the government imposes a price ceiling Pc of $2 per million BTUs. Determine the Total shortage associated with this price ceiling.
C. Calculate the non-pecuniary price.
D. Determine the full economic price? (show work)
E. How much is the social welfare loss?

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