For the pair of supply and demand equations, where x represents the quantity demanded in thousands of units and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. and

Question

For the pair of supply and demand equations, where x represents the quantity demanded in thousands of units and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.  and

Quizplus · Accepted Answer

To find the equilibrium quantity and price, we need to set the supply and demand equations equal to each other and solve for x (quantity) and p (price).
Demand: 5x + 2000 = 9000 - 4p
Supply: 3p - 6000 = 0

Setting the two equations equal to each other gives:
5x + 2000 = 3p - 6000
5x = 3p - 8000
x = (3/5)p - 1600

Plugging this equation back into either the demand or supply equation gives:
3p - 6000 = (3/5)p - 1600
(12/5)p = 4400
p = 1833.33

To find the equilibrium quantity, we plug this value of p back into our equation for x:
x = (3/5)p - 1600
x = (3/5)(1833.33) - 1600
x = 1000

Therefore, the equilibrium quantity is 1000 thousand units and the equilibrium price is $1833.33. The closest answer choice is C.

For the Pair of Supply and Demand Equations, Where X