Question

10. Let the supply and demand functions for sugar is given by the following equations. Supply: p = 1.4x - .6 Demand: p = -2x + 3.2 (a) Find the equilibrium demand. (b) Find the equilibrium price.

Answer 1

We have been given the equations for supply and demand for sugar as

`\begin{gathered} Supply\colon p=1.4x-.6 \\ Demand\colon p=-2x+3.2 \end{gathered}`

And we want to use this to find the equilibrium demand and equilibrium price.

At equiibrium price, demand and supply are equal. So we will equate the two equations to get x. The x here represents the equilibrium demand.

We have

`\begin{gathered} 1.4x-0.6=-2x+3.2 \\ 1.4x+2x=3.2+0.6 \\ 3.4x=3.8 \\ x=(3.8)/(3.4) \\ x=1.1176 \\ x=1.118 \end{gathered}`

Hence, the equilibrium demand is 1.118

So we can use any of the equations for demand or supply to find the equilibrium price. Using the first equation, we have

`\begin{gathered} p=1.4x-.6 \\ p=1.4(1.1176)-0.6 \\ p=1.56464-0.6 \\ p=0.9646 \\ p=0.96 \end{gathered}`

Hence, the equilibrium price is approximately 0.96