Question

Find the price for good Z and the quantity supply for good X (show all the calculations) if:

(i) The elasticity of supply is equal to 1 and the price increases from $40 to $50.

(ii) If the elasticity of demand is 0.5 and the quantity demanded decreases from 95.000 to 85.000.

(iii) Draw the graph and indicate the equilibrium price and quantity.

Price Per Tonne ($) Quantity Demanded Quantity Supplied

40 150 80

50 120 X

60 110 110

80 95 115

Z 85 120

110 80 140

Explain each breakdown please and watch out as some of the numbers have decimals. Thank you for the help in advance

Answer 1

Demand and Supply

Qn. i

$Elasticity\ of\ Supply(e_s)=1,\ P(\$40\to\$50)$

$e_s=\frac{\% \Delta Q_s}{\% \Delta P}=1$

${\% \Delta P}=\frac{50-40}{100}=0.1$

$1=\frac{\% \Delta Q_s}{0.1}$

$\% \Delta Q_s=\frac{X-80}{100}=0.1$

$\bold{Q_s (X)=90}$

Qn. ii

$Elasticity\ of\ Demand(e_d)=0.5,\ Q(85\to95)$

$e_d=\frac{\% \Delta Q_d}{\% \Delta P}=0.5$

${\% \Delta Q_d}=\frac{85-95}{100}=-0.1$

$0.5=\frac{-0.1}{\% \Delta P}$

$\% \Delta P=\frac{-0.1}{0.5}=-0.2$

$\therefore\ P(Z)=\frac{Z-80}{100}=-0.2$

$Z-80=-20$

$\bold{Z=60}$

Qn. iii