kinseydaviscorr
contestada

The market equilibrium point for a product is reached when 12000 units are produced and sold at $27 per unit. The manufacturer will not produce any units at the price of $6, and the customers will not buy any at the price of $69. Find the supply and demand equations, assuming they are linear.
The equations should express price p in terms of quantity q.

Supply equation: p=
Demand equation: p=

Respuesta :

taskmasters
If the equilibrium is such that only 12000 units are sold for $27, then the total earnings from the given scenario is $324,000. The supply equation would then be,
        supply: 324000 = 6p   ; p = 324000/6 = 54000
        demand: 324000 = 69p ; p = 324000/69 = 4695.65 ≈ 4696
MrRoyal

The demand and the supply equations are [tex]p = \frac{-24000 + 4000q }{7}[/tex] and [tex]p = \frac{138000 - 2000q }{7}[/tex]

How to determine the equations

At the equilibrium point, we have:

(p,q) = (12000, 27)

On the supply equation, we have:

(p,q) = (0, 6)

So, we start by calculating the slope:

[tex]m = \frac{q_2 - q_1}{p_2 -p_1}[/tex]

This gives

[tex]m = \frac{6 - 27}{0 - 12000}[/tex]

[tex]m = \frac{21}{12000}[/tex]

Simplify

[tex]m = \frac{7}{4000}[/tex]

The supply equation is then calculated as:

[tex]q = m(p - p_1) + q_1[/tex]

So, we have:

[tex]q = \frac{7}{4000}(p - 0) + 6[/tex]

[tex]q = \frac{7}{4000}p + 6[/tex]

Subtract 6 from both sides

[tex]-6 + q = \frac{7}{4000}p[/tex]

Multiply through by 4000

[tex]-24000 + 4000q = 7p[/tex]

Rewrite as:

[tex]7p = -24000 + 4000q[/tex]

Solve for p

[tex]p = \frac{-24000 + 4000q }{7}[/tex]

On the demand equation, we have:

(p,q) = (0, 69)

So, we start by calculating the slope:

[tex]m = \frac{q_2 - q_1}{p_2 -p_1}[/tex]

This gives

[tex]m = \frac{69 - 27}{0 - 12000}[/tex]

[tex]m = -\frac{42}{12000}[/tex]

Simplify

[tex]m = -\frac{7}{2000}[/tex]

The demand equation is then calculated as:

[tex]q = m(p - p_1) + q_1[/tex]

So, we have:

[tex]q = -\frac{7}{2000}(p - 0) + 69[/tex]

[tex]q = -\frac{7}{2000}p + 69[/tex]

Subtract 69 from both sides

[tex]-69 + q = -\frac{7}{2000}p[/tex]

Multiply through by -2000

[tex]138000 - 2000q = 7p[/tex]

Rewrite as:

[tex]7p = 138000 - 2000q[/tex]

Solve for p

[tex]p = \frac{138000 - 2000q }{7}[/tex]

Hence, the demand and the supply equations are [tex]p = \frac{-24000 + 4000q }{7}[/tex] and [tex]p = \frac{138000 - 2000q }{7}[/tex]

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