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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.

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Answer:

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

abidemiokin

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 :

  • Supply function: 4p - q = 44

  • Demand function: (p + 2)q = 1680

where:

  • p  is the price
  • q is the quantity

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

Learn more on-demand function here: https://brainly.com/question/15234429

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