For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Question

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.

2x + 9p - 93 = 0 and 3x - 14p + 108 = 0

a. equilibrium quantity 12,000 units; equilibrium price $9

b. equilibrium quantity 12,000 units; equilibrium price $13

c. equilibrium quantity 6,000 units; equilibrium price $13

d. equilibrium quantity 6,000 units; equilibrium price $9

Please explain. thank you

Answer 1

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Answer 2

To find the equilibrium quantity and the equilibrium price, we need to solve the system of equations:

2x + 9p - 93 = 0 ......(1)
3x - 14p + 108 = 0 .......(2)

Let's solve this system using the method of substitution:

From equation (1), we can rewrite it as:
2x = 93 - 9p
x = (93 - 9p)/2

Now substitute this value of x in equation (2):
3((93 - 9p)/2) - 14p + 108 = 0

Multiply both sides by 2 to eliminate the fraction:
3(93 - 9p) - 28p + 216 = 0
279 - 27p - 28p + 216 = 0
495 - 55p = 0
55p = 495
p = 495/55
p = 9

Now substitute this value of p back into equation (1):
2x + 9(9) - 93 = 0
2x + 81 - 93 = 0
2x - 12 = 0
2x = 12
x = 12/2
x = 6

Therefore, the equilibrium quantity is 6,000 units and the equilibrium price is $9.

So, the correct answer is (d) equilibrium quantity 6,000 units; equilibrium price $9.

Answer 3

To find the equilibrium quantity and price, we need to solve the system of equations:

2x + 9p - 93 = 0 (Equation 1)
3x - 14p + 108 = 0 (Equation 2)

First, let's solve Equation 1 for x:
2x + 9p - 93 = 0
2x = -9p + 93
x = (-9p + 93)/2

Next, substitute this value of x into Equation 2:
3((-9p + 93)/2) - 14p + 108 = 0
((-27p + 279)/2) - 14p + 108 = 0
(-27p + 279) - 28p + 216 = 0
-55p + 495 = 0
55p = 495
p = 495/55
p = 9

Now that we have the value of p, we can substitute it back into Equation 1 to find x:
2x + 9(9) - 93 = 0
2x + 81 - 93 = 0
2x - 12 = 0
2x = 12
x = 12/2
x = 6

Therefore, the equilibrium quantity is 6,000 units (since x represents quantities in 1,000s) and the equilibrium price is $9.

The correct answer is:

d. equilibrium quantity 6,000 units; equilibrium price $9