In 2010 Americans smoked 315 billion cigarettes or 1575 bill

In 2010, Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The average retail price (including taxes) was about $5 per pack. Statistical studies have shown that the price elasticity of demand is roughly 0.35, and the price elasticity of supply is about 0.50. Using this information, derive linear demand and supply curves for the cigarette market. Let the demand curve be of the genera for:Qa-bP and the supply curve be of the general form: Q-c+dP where Q is billions of packs of cigarettes and a, b, c, and d are constants. The equation for the demand curve is OA. O B. Q 21.2625-1.1025P. Q-21.2625 + 1.1025P. O C. Q 5.5125-21.2625P. O D. Q 5.5125-1.1025P E· Q-212625-1.575P

Solution

Option (A).

Demand curve equation: Q = a - bP

Elasticity of demand = (dQ/dP) x (P/Q) = - b x (P/Q)

Plugging in given values,

- 0.35 = - b x (5 / 15.75)

5b = 0.35 x 15.75

5b = 5.5125

b = 1.1025

Therefore,

15.75 = a - 1.1025 x 5

15.75 = a - 5.5125

a = 21.2625

Linear demand equation is:

Q = 21.2625 - 1.1025P