Question

1. You have been asked to analyze the market for steel. From public sources, you are able to find that last year’s price for steel was $20 per ton. At this price, 100 million tons were sold on the world market. From trade association data you are able to obtain estimates for the own price elasticities of demand and supply on the world markets as −0.25 for demand and 0.5 for supply. Assume that steel has linear demand and supply curves throughout.
2. (a) (10 points) Solve for the equations of demand and supply in this market and sketch the demand and supply curves.

Answer 1

Assume that this is a competitive market and demand and supply are liner.

$X_d = a -bP \\ X_s = c + dP$

We know from the equation for own-price elasticity of demand that:

$E_{QxPx}= \frac{dX_d}{dP_X} \frac{P_X}{X_d}=-b\frac{P_X}{X_d}=-b\frac{20}{100}=-0.25 \\ b = 1.25 \\ QX_d = a -1.25P \\ 100 = a -1.25 \times 20 \\ a = 125$

Equation of the demand curve will be

$QX_d = 125 -1.25P$

Similarly for the price elasticity of supply we have:

$E_{QxPx}=\frac{dX_s}{dP_X} \frac{P_X}{X_s} = d\frac{20}{100}=0.5 \\ d = 2.5 \\ QX_s = c+2.5P \\ 100 = c + 2.5 \times 20 \\ c = 50$

The equation for last year’s supply will be:

$QX_s = 50 + 2.5P$