Solve the problem.
-Assume that the price per unit d of a certain item to the consumer is given by the equation d = 35 - .10x, where x is the number of units in demand. The price per unit from the supplier is given by the equation s = .2x + 20,
Where x is the number of units supplied. Find the equilibrium price and the equilibrium quantity.
A) equilibrium price: $35 per unit; equilibrium quantity: 50 units
B) equilibrium price: $50 per unit; equilibrium quantity: 30 units
C) equilibrium price: $30 per unit; equilibrium quantity: 50 units
D) equilibrium price: $20 per unit; equilibrium quantity: 50 units

Question

Quizplus · Accepted Answer

The equilibrium price and quantity occur when the price per unit from the supplier equals the price per unit to the consumer. Therefore, set d equal to s:
35 - 0.10x = 0.2x + 20
Combine like terms:
0.30x = 15
x = 50
Substitute x = 50 into either equation to find the equilibrium price:
d = 35 - 0.10(50) = 30
Therefore, the equilibrium price is $30 per unit and the equilibrium quantity is 50 units. The correct answer is C. The equilibrium price and quantity occur where the demand and supply curves intersect. So we need to find the x that satisfies the equation d = s.

35 - .10x = .2x + 20

Solving for x, we get x = 150.

So the equilibrium quantity is 150 units.

To find the equilibrium price, we substitute x = 150 into either the demand or supply equation. Let's use the demand equation:

d = 35 - .10(150) = $20 per unit

So the equilibrium price is $20 per unit.

Therefore, the answer is C: equilibrium price: $30 per unit; equilibrium quantity: 50 units.

Solve the Problem. -Assume That the Price Per Unit D of a Certain