MHB How to Solve for Equations of Demand and Supply with Given Price Elasticity?

[abigmole]

The current price in the market for bananas is $0.10 per pound. At
this price, 1 million pounds are sold per year in Small-town, Malaysia.
Suppose that the price elasticity of demand is -5 and the short run
price elasticity of supply is 0.05. Solve for the equations of demand
and supply, assuming that demand and supply are linear.Hi, was given this question to do and I'm lost! Anyone knows how to solve this?

Would greatly appreciate any form of help! Thanks!

 

[Sudharaka]

The current price in the market for bananas is $0.10 per pound. At
this price, 1 million pounds are sold per year in Small-town, Malaysia.
Suppose that the price elasticity of demand is -5 and the short run
price elasticity of supply is 0.05. Solve for the equations of demand
and supply, assuming that demand and supply are linear.Hi, was given this question to do and I'm lost! Anyone knows how to solve this?

Would greatly appreciate any form of help! Thanks!

Hi abigmole, :)

Let \(P\) be the price, \(Q_{d}\) be the quantity demanded and \(Q_{s}\) be the quantity supplied. Since the demand and supply curves are linear those curves could be represented by,

\[P=aQ_{d}+b\mbox{ and }P=cQ_{s}+d\]

The elasticity of demand and supply are defined by,

\[E_{d}=\frac{P}{Q_{d}}\frac{dQ_{d}}{dP}\mbox{ and }E_{s}=\frac{P}{Q_{s}}\frac{dQ_{s}}{dP}\]

\[\therefore E_{d}=\frac{1}{a}\frac{P}{Q_{d}}\mbox{ and }E_{s}=\frac{1}{c}\frac{P}{Q_{s}}\]

It is given that \(E_{d}=-5\mbox{ and }E_{s}=0.05\). Since this market is in a economic equilibrium situation, \[\frac{P}{Q_{d}}=\frac{P}{Q_{s}}=\frac{0.1\times 10^{6}}{10^{6}}=0.1\]

I hope you can do the rest yourself. You have to find the values of \(a\) and \(b\). Then consider the equilibrium point so that you can solve for \(c\) and \(d\) in the supply and demand curves.

Kind Regards,
Sudharaka.