Question

11. Let the supply and demand functions for sugar is given by the following equations. Supply: p = 0.4x Demand: p = 100 - 0.4x (a) Find the equilibrium demand.

Answer 1

Step 1:

In this question, we are given the following:

Let the supply and demand functions for sugar be given by the following equations. Bye

Supply: p = 0.4x

Demand: p = 100 - 0.4x

a) Find the equilibrium demand.

Step 2:

At Equilibrium,

`\begin{gathered} \text{Supply}=\text{ Demand} \\ 0.\text{ 4 x = 100 - 0. 4 x} \end{gathered}`

collecting like terms, we have that:

`\begin{gathered} 0.4\text{ x + 0. 4 x = 100} \\ 0.8\text{ x = 100} \end{gathered}`

Divide both sides by 0.8, we have that:

`\begin{gathered} x\text{ = }\frac{100}{0.\text{ 8}} \\ x\text{ = 125} \end{gathered}`



Step 3:

Recall that:

`\begin{gathered} \text{Equilibrium Demand : p = 100 - 0. 4 x } \\ we\text{ put x = 125, we have that:} \\ p\text{ = 100 - 0. 4 (125)} \\ p\text{ =100 -50} \\ p\text{ = 50} \end{gathered}`

CONCLUSION:

Equilibrium Demand:

`p\text{ = 50 units}`