In 2007, Americans smoked 19.219.2 billion packs of cigarettes. They paid an average retail price of $4.504.50 per pack. a. Given that the elasticity of supply is 0.50.5 and the elasticity of demand is negative 0.4−0.4, derive linear demand and supply curves for cigarettes. The demand equation is

equation for demand is Q=26,906,880,000,150 - 1,706,666,666.7P

equation for supply is Q=9,609,600,000,150.2 + 2,133,333,333.3P

Pls find all other required parameters in the explanation

Explanation:

Let the demand curve be of the general form Q = a - bP

Let the supply curve be of the general form Q = c + dP

where a, b, c, and d are the constants that you have to find from the information given in the equation

To begin, recall the formula for the price elasticity of demand

E = (P/Q)(ΔQ/ΔP)

Where P is the price per pack = $4,504.50

Q is the quantity of packets= 19,219.2 billion

You are given information about the value of the elasticity E as -0.4

So solve for the slope, which is b in the above formula for the demand curve using the equation E = (P/Q)(ΔQ/ΔP

−0.4 = ($4,504.50/19,219200000000)(ΔQ/ΔP)

ΔQ/ΔP = −0.4(19,219200000000/$4,504.50)

= −1,706,666,666.7= −b.

To find the constant a, substitute for Q, P, and b into the demand curve formula

Q = a - bP

so

19,219200000000 = a - 1,706,666,666.7 × 4,504.50

19,219200000000 = a - 7,687,680,000,150.1

a = 19,219200000000 + 7,687,680,000,150.1

a = 26,906,880,000,150

The equation for demand is therefore

Q=26,906,880,000,150 - 1,706,666,666.7P.

To find the supply curve,

recall the formula for the elasticity of supply and follow the same method as above: E = 0.5

E= (P/Q)(ΔQ/ΔP)

0.5 = ($4,504.50/19,219200000000)(ΔQ/ΔP)

ΔQ/ΔP = 0.5(19,219200000000/$4,504.50)

= 2,133,333,333.3 = d.

To find the constant c, substitute for Q, P, and d into the supply curve formula

Q = c + dP so that

19,219200000000 = c + 2,133,333,333.3 × 4,504.50

19,219200000000 = c + 9,609,599,999,849.8

c = 9,609,600,000,150.2

The equation for supply is therefore Q=9,609,600,000,150.2 + 2,133,333,333.3P.

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