Question

3) Suppose that the market demand for Blue band is a straight line of the form Q = 300-50p where Q is the quantity bought in thousands of boxes per week and P is the price per box in. i. How much Blue Band is demanded at P= 0?

ii. At what price does the demand for Blue Band go to zero?

iii. Calculate total expenditures for Blue Band at each price between and inclusive of the prices identified in parts

(i) and (ii) above. iv. Is demand elastic or inelastic at the following prices; (a) P =2 (b) P=4. Explain your answers.

Answer 1

$(I) Q=300-50P\\P=0\\Q=300-50(0)\\Q=300$

$(ii) Q=0\\0=300-50P\\300=50P\\P=6$

$(iii) Expenditure=Quantity×Price\\ at \space P=0,Q=300\\=300×0=0$

$at \space P=1,Q=300-50(1)=300\\=250×1=250\\ at \space P=2,Q=300-50(2)=200\\=200×2=400\\ at \space P=3,Q=300-50(3)=150\\=150×3=450\\ at \space P=4,Q=300-50(4)=100\\=100×4=400\\ at \space P=5,Q=300-50(5)=50\\=50×5=250\\$

$at \space P=6,Q=0\\=6×0=0$

$iv)\\ at \space P=2\\Q=300-50(2)\\=300-100\\Q=200\\ at \space P=4\\Q=300-50(4)\\=300-200\\Q=100$

Elasticity of demand$=\frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}} {\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

$=\frac{\frac{100-200}{\frac{100+200}{2}}} {\frac{4-2}{\frac{4+2}{2}}}\\ \frac{-0.67}{0.67}\\=-1\\ Demand \space is \space inelastic$