If the supply and demand functions for a commodity are given by 4p − q = 44 and (p + 2)q = 1,680, respectively, find the price and quantity that will result in market equilibrium.

The price and quantity that will result in market equilibrium are 26 and 60 respectively

Demand and supply function

Given the demand and supply functions :

where:

Expressing supply function in terms of q

4p - 44 = q - - - - - (2)

4p - 44 = q

Substitute into equation 1 we will ha

(p + 2) (4p - 44) = 1680

4p²- 44p + 8p - 88 = 1680

4p² - 36p - 1768 = 0

p² - 9p - 442p = 0

Factorize the result to have:

p(p - 26) + 17(p-26) = 0

(p + 17) = 0 ; (p - 26) =0

p = - 17 or p = 26

Since the price of a commodity can't be negative, Hence, p = 26

Recall that q = 4p - 44

q = 4(26) - 44

q = 104 - 44

q = 60

Hence the price and quantity that will result in market equilibrium are 26 and 60 respectively

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p = 26 ; q = 60

Step-by-step explanation:

Given the demand and supply functions :

Supply function:

4p - q = 44

Demand function :

(p + 2)q = 1680 - - - - (1)

p = price ; q = quantity

Expressing supply function interms of q

4p - 44 = q - - - - - (2)

Plug 4p - 44 = q into (1)

(p + 2) (4p - 44) = 1680

4p²- 44p + 8p - 88 = 1680

4p² - 36p - 1768 = 0

p² - 9p - 442p = 0

p(p - 26) + 17(p-26) = 0

(p + 17) = 0 ; (p - 26) =0

p = - 17 or p = 26

Price of commodity can't be negative, Hence, p = 26

From q = 4p - 44

Put p = 26

q = 4(26) - 44

q = 104 - 44

q = 60

p = 26 ; q = 60

45 degres

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