Barbara has estimated the demand and marginal revenue for her product.They are P = 84 - 2Q (quantity) and MR = 84 - 4Q, respectively.She also experiences a constant marginal cost of $16.What is Barbara’s profit-maximising quantity and price?Question 4Answera.Q = 12; P = $50b.Q = 12; P = $40c.Q = 17; P = $50d.Q = 17; P = $40
Question
Barbara has estimated the demand and marginal revenue for her product.They are P = 84 - 2Q (quantity) and MR = 84 - 4Q, respectively.She also experiences a constant marginal cost of 50b.Q = 12; P = 50d.Q = 17; P = $40
Solution
Para encontrar la cantidad y el precio que maximizan el beneficio de Barbara, debemos igualar el ingreso marginal (MR) al costo marginal (MC).
Dado:
- MR = 84 - 4Q
- MC = $16
Igualamos MR a MC: 84 - 4Q = 16
Resolvemos para Q: 84 - 16 = 4Q 68 = 4Q Q = 68 / 4 Q = 17
Ahora, usamos la función de demanda para encontrar el precio correspondiente a esta cantidad: P = 84 - 2Q P = 84 - 2(17) P = 84 - 34 P = 50
Por lo tanto, la cantidad que maximiza el beneficio es 17 y el precio es $50.
La respuesta correcta es: c. Q = 17; P = $50
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