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suppose that in the market for good x there are 4000 consumers with an individual demand curve given by q d 30 0 75p there

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Suppose that in the market for good X there are 4000 consumers, with an individual demand curve given by: 𝑄 𝐷 = 30 − 0.75𝑃. There are also 100 producers, each of which has a supply curve given by: 𝑄 𝑆 = −300 + 20𝑃 Page 5 of 12 2.1.1. Determine the equilibrium price and quantity in this Marketplace. Represent graphically.

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Answer to a math question Suppose that in the market for good X there are 4000 consumers, with an individual demand curve given by: 𝑄 𝐷 = 30 − 0.75𝑃. There are also 100 producers, each of which has a supply curve given by: 𝑄 𝑆 = −300 + 20𝑃 Page 5 of 12 2.1.1. Determine the equilibrium price and quantity in this Marketplace. Represent graphically.

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Dado que existem 4000 consumidores, a curva agregada de procura \( Q_D \) é:

Q_D = 4000 (30 - 0.75P)

Dado que existem 100 produtores, a curva agregada de oferta \( Q_S \) é:

Q_S = 100 (-300 + 20P)

Para encontrar o equilíbrio, igualamos \( Q_D \) e \( Q_S \):

4000(30 - 0.75P) = 100(-300 + 20P)

Resolvendo a equação acima:

120000 - 3000P = -30000 + 2000P

120000 + 30000 = 5000P

150000 = 5000P

P = 30

Substituindo o valor de \( P \) em \( Q_D \) ou \( Q_S \):

Q_D = 4000(30 - 0.75 \cdot 30)

Q_D = 4000(30 - 22.5)

Q_D = 4000 \cdot 7.5

Q_D = 30000

Portanto, a quantidade de equilíbrio é:

Q = 30000

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