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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.

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

 

                                 Qs = 14 + 2 PG + .25 P0          Qd = -5 PG + 3.75 P0

 

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

   of cubic feet), PG represents the price of natural gas (per cubic foot) and P0 represents the

   price of oil (per barrel).

 

a) If P0 = 6, find the equilibrium price and quantities of natural gas.

 

b) Find the new equilibrium price and quantities if P0 doubles (from 6 to 12).

 

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

 

                                   QD = 400 - 25 P + 0.4 M + 24 PR

 

                                   QS = 48 + 12 P -20 PI + 20 F

 

QD = quantity demanded; P = price of the commodity; M = average household income;

PR = Price of related goods in consumption (complements or subsititutes); QS = quantity

supplied; PI = Factor or input prices; F = Number of suppliers

 

a. Initially, M = $61,140 and PR = $6. Find the "reduced" demand equation.

b. Find the inverse demand function (in which P is a function of QD).

c. Initially, PI = $25 and F = 22.  Find the "reduced" supply equation

d. Find the inverse supply equation (in which P is a function of QS).

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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