The market of natural gas is described by the following supply and demand equations:

Qs = 14 + 2 P_{G }+ .25 P_{0} Qd = -5 P_{G} + 3.75 P_{0}

where Qs represent the quantities supplied and demanded of natural gas (in millions

of cubic feet), P_{G }represents the price of natural gas (per cubic foot) and P_{0} represents the

price of oil (per barrel).

a) If P_{0} = 6, find the equilibrium price and quantities of natural gas.

b) Find the new equilibrium price and quantities if P_{0} doubles (from 6 to 12).

**5.** The generalized demand and supply functions for a commodity are

Q_{D} = 400 - 25 P + 0.4 M + 24 P_{R}

Q_{S} = 48 + 12 P -20 P_{I} + 20 F

Q_{D} = quantity demanded; P = price of the commodity; M = average household income;

P_{R} = Price of related goods in consumption (complements or subsititutes); Q_{S} = quantity

supplied; P_{I} = Factor or input prices; F = Number of suppliers

a. Initially, M = $61,140 and P_{R} = $6. Find the "reduced" demand equation.

b. Find the inverse demand function (in which P is a function of Q_{D}).

c. Initially, P_{I} = $25 and F = 22. Find the "reduced" supply equation

d. Find the inverse supply equation (in which P is a function of Q_{S}).

e. Will a price of $600 cause a shortage or surplus? How much?

f. Find the market equilibrium price and quantity.

Now, let the number of firms increase to 133.

g. Find the new supply equation. What are the new equilibrium price and quantity.

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Supply and demand equations are used for calculating equilibrium prices and quantity. It is because the point... View the full answer