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When gas prices are $2.73 per gallon, the annual supply for gas in New York State is 135 billion gallons and the annual
demand is 141 billion gallons. When the price increases to $3.26 per gallon, the annual supply increases to 147 billion gallons and the
demand decreases to 137 billion gallons.
(a) Assuming that the supply and demand equations are linear, Ofind the supply and demand equations.
Supply Equation p =
Demand Equation p =
Note: The equations should be in the form p = mq + b where p denotes the price (in dollars) and q denotes the quantity (in billions).
The slope and y-intercept should include 3 decimal places, or be left as fractions.
(b) Find the market price and quantity.
market price p =
market quantity q =
Note: The market price and quantity should include 3 decimal places (or left as fractions), and the market price should include a dollar
sign.

Sagot :

The supply equation is p = 0.044q - 3.21.

How to compute the supply equation?

The supply will be:

p = mq + b

2.73 = 135m + b

3.26 = 147m + b

Subtract both equations

12m = 0.53

m = 0.53/12

m = 0.044

We'll substitute it and this will be:

2.73 = 135m + b

2.73 = 135(0.044) + b

2.73 = 5.94 + b

b = -5.94 + 2.73 = -3.21

The supply equation will be

p = mq + b

p = 0.044q - 3.21

The demand equation will be:

2.73 = 141m + b

3.26 = 137m + b

Subtract the equations

4m = -0.53

m = -0.1325

2.73 = 141m + b

2.73 = 141(-0.1325) + b

b = 2.73 + 18.68

b = 21.41

The demand equation will be

p = -0.1325q + 21.41.

The equilibrium condition will be:

0.044q - 3.21 = -0.1325q + 21.41.

0.044q + 0.1325q = 21.41 + 3.21

0.1765q = 24.62

q = 140

Equilibrium quantity = 140

The market price will be:

p = 0.044q - 3.21

p = 0.044(140) - 3.21

p = 2.95

The market price is 2.95.

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