From the diagram, the demand curve DD cuts the original supply curve SS at the initial equilibrium of quantity \(30\) tonnes and price \(\$100\) per tonne. When supply shifts to \(S_1S_1\), the new equilibrium is at quantity \(40\) tonnes and price \(\$40\) per tonne. All working below uses these read-off values.
(a)(i) Total revenue at the initial equilibrium
Total revenue is price multiplied by quantity sold, \(TR = P \times Q\).
\[TR = \$100 \times 30 = \$3{,}000\]
The farmer earns \(\$3{,}000\) at the initial equilibrium.
(a)(ii) Total revenue after supply shifts to \(S_1S_1\)
\[TR_1 = \$40 \times 40 = \$1{,}600\]
After the shift the farmer earns \(\$1{,}600\).
(b) Change in total revenue when price falls from \(\$100\) to \(\$40\) per tonne
\[\Delta TR = TR_1 - TR = \$1{,}600 - \$3{,}000 = -\$1{,}400\]
Total revenue falls by \(\$1{,}400\). Notice that although more maize is now sold (\(40\) tonnes instead of \(30\)), revenue still drops. This happens because the price cut of \(60\%\) is far larger in proportion than the rise in quantity, which is the tell-tale sign of an inelastic demand, confirmed below.
(c)(i) Price elasticity of demand for maize
Elasticity is measured along the demand curve DD, using the two price-quantity points it passes through: \((P=100,\ Q=30)\) and \((P=40,\ Q=40)\). Taking the first point as the base:
\[E_d = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \frac{\Delta Q / Q_1}{\Delta P / P_1}\]\[\Delta Q = 40 - 30 = 10, \qquad \Delta P = 40 - 100 = -60\]\[E_d = \frac{10/30}{-60/100} = \frac{0.3333}{-0.6} = -0.56\]
Ignoring the negative sign (which merely reflects the downward-sloping demand curve), \(|E_d| \approx \mathbf{0.56}\).
(c)(ii) Interpretation
Since \(|E_d| = 0.56 < 1\), the demand for maize is price inelastic. A \(1\%\) change in price brings about only about a \(0.56\%\) change in quantity demanded, so buyers are not very responsive to price changes. This is typical of a food staple like maize, and it explains the paradox in part (b): cutting the price shrinks the farmer's total revenue rather than raising it.
(d) Two reasons for the shift of supply from SS to \(S_1S_1\)
The curve shifts outward to the right, meaning more is supplied, so the causes are factors that make production easier or cheaper:
- Favourable weather / good rainfall during the growing season, giving a larger harvest at every price.
- A fall in the cost of production (for example cheaper fertiliser, seeds or fuel) or a government subsidy to maize farmers, both of which raise the quantity farmers are willing to supply. Improved technology or high-yield seed varieties would have the same effect.
