The market equilibrium price is $9 and the quantity is 28 dozens of cookies. The consumer surplus and producer surplus are both $98, and there is no deadweight loss since the market is in equilibrium. When considering the external marginal benefits, the equilibrium price is still $9 but the quantity increases to 36 dozens of cookies. The consumer surplus and producer surplus remain the same at $98, and there is still no deadweight loss.
A. Find the market equilibrium price and quantity of cookies?
To find the market equilibrium price and quantity, we need to set the demand equal to the marginal cost:
16 - 0.25Q = 2 + 0.25Q
Combining like terms:
16 - 2 = 0.25Q + 0.25Q
14 = 0.5Q
Dividing both sides by 0.5:
Q = 28
Now, substituting this value back into the demand equation to find the price:
P = 16 - 0.25 * 28
P = 16 - 7
P = 9
Therefore, the market equilibrium price is $9 and the quantity is 28 dozens of cookies.
B. What is the consumer surplus, producer surplus, and deadweight loss in the market?
To find the consumer surplus, we need to calculate the area under the demand curve and above the market price. The formula for consumer surplus is: (0.5 * (16 - 9) * 28) = $98.
To find the producer surplus, we need to calculate the area above the supply curve and below the market price. The formula for producer surplus is: (0.5 * (9 - 2) * 28) = $98.
Deadweight loss represents the loss in total surplus when the market is not in equilibrium. In this case, the deadweight loss is zero since the market is in equilibrium.
C. If the bakeries consider the external marginal benefits of baking cookies, what is the equilibrium price and quantity of cookies?
If the bakeries consider the external marginal benefits, we need to add the external benefit to the demand equation:
P = 16 - 0.25Q + 2
Combining like terms:
P = 18 - 0.25Q
Setting this equal to the marginal cost:
18 - 0.25Q = 2 + 0.25Q
Combining like terms:
18 = 0.5Q
Dividing both sides by 0.5:
Q = 36
Now, substituting this value back into the demand equation to find the price:
P = 18 - 0.25 * 36
P = 18 - 9
P = 9
Therefore, the equilibrium price is $9 and the quantity is 36 dozens of cookies.
D. What is the consumer surplus, producer surplus, and deadweight loss in the market when the bakeries consider the external marginal benefits of baking cookies?
To find the consumer surplus, we can use the same formula as before since the market price is unchanged at $9.
To find the producer surplus, we also use the same formula as before.
Deadweight loss is still zero since the market is in equilibrium.