Question

the market for juice is represented by the following functions Q+1/3p= 36, Q+9=1/2p where p= price Q = quantity.

i. identify the demand and supply functions, giving reasons in each case

ii. determine the equilibrium price and quantity

iii. calculate the price elasticity of demand for juice, when its price changes from shs. 30 to shs. 36

Answer 1

i.

$Q+\frac{1}{3}p= 36, -demand\\ Q+9=\frac{1}{2}p-supply$

ii.

$108-3Q=2Q-18\\108+18=2Q+3Q\\126=5Q\\Q=25.2\\p=2Q-18\\=2(25.2)-18\\p=32.4$

iii.

$P=30\\30=2Q-18\\48=2Q\\Q=24\\P=36\\ 36=2Q-18\\54=2Q\\Q=27\\$

$=\frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}}{\frac{p_2-p_1}{\frac{p_2+p_1}{2}}}\\ =\frac{\frac{27-24}{\frac{27+24}{2}}}{\frac{36-30}{\frac{36+30}{2}}}\\ \frac{\frac{3}{25.5}}{\frac{3}{33}}=1.29$