Question

Learning outcome: Solve a linear system of equations in two and three variables using algebraic methods. Read and solve word problems by modeling them with systems of linear equations. Activity: Let p represent the selling price for a bluetooth device. Suppose that the demand equation for this device can be modeled as the linear function D(p) = 200- 5p and that the supply equation for the same device as S(p) = 10p. Find the equilibrium price and quantity for this device keeping in mind that at market equilibrium demand equals supply.

Answer 1

Answer: Equilibrium price would be $13.33 and equilibrium quantity would be 133.3 units.

Explanation:

Since we have given that

Demand function is stated as

`D(p)=200-5p`

Supply function is stated as

`S(p)=10p`

We need to find the equilibrium price and quantity for this device.

For equilibrium, D(p) = S(p).

so, it becomes,

`200-5p=10p\\\\200=10p+5p\\\\200=15p\\\\p=(200)/(15)\\\\p=\$13.33`

and when we put the value of p in any function:

`Q=10* 13.33=133.3\ units`

Hence, Equilibrium price would be $13.33 and equilibrium quantity would be 133.3 units.