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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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.
Hermann
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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
Dado que existem 100 produtores, a curva agregada de oferta \( Q_S \) é:
Para encontrar o equilíbrio, igualamos \( Q_D \) e \( Q_S \):
Resolvendo a equação acima:
Substituindo o valor de \( P \) em \( Q_D \) ou \( Q_S \):
Portanto, a quantidade de equilíbrio é:
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