11.07.2022 - 04:23

# Suppose the factory Afro-Puffs Inc. produces wigs. As a by-product of this wig production, they also produce dangerous emissions of toxic gases (as a result of the strong glue used to hold the hair in place). The De-Lite car factory, down the road, experi

Question:

Suppose the factory Afro-Puffs Inc. produces wigs. As a by-product of this wig production, they also produce dangerous emissions of toxic gases (as a result of the strong glue used to hold the hair in place). The De-Lite car factory, down the road, experiences a negative externality from this production process. Suppose that the supply curve (private marginal costs) for the wig factory is Qs = (2/5)P – 2, and it faces a market demand of Qd = 15 – P/2. The marginal damages caused by the production of wigs can be written as P = Q + 1/2.

a. Find the equilibrium price and quantity in the market for wigs .

b. Find the socially optimal level of wigs and the corresponding price.

• April 1, 2023 в 21:01
a. To find the equilibrium price and quantity in the market for wigs, we need to find where the supply and demand curves intersect. So, we set Qs equal to Qd: (2/5)P - 2 = 15 - P/2 Multiplying both sides by 10, we get: 4P - 40 = 150 - 5P Bringing all the P terms to the left side and all the constant terms to the right side, we get: 9P = 190 P = 21.11 Substituting this back into either the supply or demand equation, we get: Q = (2/5)(21.11) - 2 = 6.44 So, the equilibrium price is $21.11 and the equilibrium quantity is 6.44 wigs. b. The socially optimal level of wigs is where the marginal damages caused by production (which represent the social cost) are equal to the private marginal costs. So, we set P (which represents the marginal damages) equal to the supply curve: Q + 1/2 = (2/5)P - 2 Multiplying both sides by 10, we get: 5Q + 5 = 4P - 40 Bringing all the Q terms to the left side and all the constant terms to the right side, we get: 5Q - 4P = -45 We also know that the social demand is given by Qd = 15 - P/2, so we can substitute this in for Q: 5(15 - P/2) - 4P = -45 Simplifying, we get: P = 18.75 Substituting this back into the social demand equation, we get: Q = 7.63 So, the socially optimal level of wigs is 7.63, and the corresponding price is$18.75. This is higher than the equilibrium price of \$21.11, indicating that the market is producing too few wigs from a social perspective.
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