The supply of coffee is Qs 2002P where quantity is in billio

The supply of coffee is Q_s= 2.0+0.2P, where quantity is in billions of pounds and price is dollars per pound. The price elasticity of demand for coffee is about -0.3, the current price is $3.00 per pound and the quantity bought and sold is 2.6 billion pounds. Based on this information, the linear demand curve for coffee is Q_D= ___ - ___ P. (Enter your responses-- the intercept and slope-- as real numbers rounded to 2 decimal places. Note that a negative sign already appears in front of the slope term, so enter your slope coefficient as a positive number.)

A severe drought reduces the price of coffee by 10% at every price. The new equilibrium price of coffee will be $____ , and the new equilibrium quantity will be ___billion pounds. (Enter your responses as real numbers rounded to 2 decimal places.)

Solution

Elasticity of demand = (dQ/dP)*P\'/Q\'

where P\'= initial price

Q\' =Initial quantity

dQ/dP = -0.3(2.6/3) = -0.26

Equation of demand for coffee:

Q - 2.6 = (-0.26)(P - 3)

Qd = 3.38 - 0.26P

New price of coffee = 3 - 0.3 = $2.7

2+0.2(9/10P) = 3.38 - 0.26(9/10P)

2+0.13P = 3.38 - 0.14P

P =3.45

Equilibrium price = 3.45 - 0.34 = 3.1

Equilibrium quantity = 2.62