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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.

Hermann
4.6
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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