Question

The supply of coffee is Qs 2.0+0.2P, where quantity is in billions of pounds and price is dollarsper 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 apP (Entor your responsos-the intercept and slope-as roal 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 supply of coffee by 10 percent at overy prico. The new equilibrium price of coffee will be s numbers rounded to 2 decimal places.) and the new equilibium quantity will be billion pounds. (Entor your responsos as roal

Answer 1

(1) Equation of linear demand curve: QD = a - bP

Elasticity = (dQD/dP) x (P/QD) = -b x [P / (a - bP)] = -0.3

-b x [3 / (a - 3b)] = -0.3

b / (a - 3b) = 1

b = a - 3b

4b = a

Also, when P = 3, QD = 2.6 (billion)

2.6 = a - 3b

2.6 = 4b - 3b

b = 2.6

a = 4 x 2.6 = 10.4

Linear demand curve: QD = 10.40 - 2.60P

(2) New supply function: QS(New) = 0.9 x QS(Old)

QS(New) = 0.9 x (2 + 0.2P)

QS(New) = 1.8 + 0.18P

Equating with QD,

10.4 - 2.6P = 1.8 + 0.18P

2.78P = 8.6

P = 3.09

Q = 10.4 - (2.6 x 3.09) = 10.4 - 8.03 = 2.37 (billion pounds)