Question

The inverse demand function for lemons is defined by the equation p = 120 − 11q, where q is the number of crates that are sold. The inverse supply function is defined by p = 8 + 3q. In the past there was no tax on lemons but now a tax of $84 per crate has been imposed. What are the quantities produced before and after the tax was imposed?

Answer 1

The equilibrium quantity of lemons produced before the tax is 8 crates, and after an $84 per crate tax is imposed, it drops to 2 crates.

Step-by-step explanation:

To find the quantities produced before and after the tax was imposed on lemons, we need to solve for the equilibrium quantities using the inverse demand and inverse supply functions. The equilibrium quantity before the tax is where the quantity demanded equals the quantity supplied, so we set the demand function equal to the supply function.

For the inverse demand function p = 120 - 11q and the inverse supply function p = 8 + 3q, we calculate:

1. Set them equal to each other: 120 - 11q = 8 + 3q.
2. Solve for q: 112 = 14q.
3. Divide both sides by 14: q = 8.

So, 8 crates of lemons are produced before the tax.

After an $84 per crate tax is imposed, the supply function becomes p = 8 + 3q + 84 because the tax is added to the cost of production, which shifts the supply curve up by the amount of the tax. Now, the new equilibrium is found by setting the new supply function equal to the demand function.

1. Include tax in the supply function: 120 - 11q = 8 + 3q + 84.
2. Solve for q: 28 = 14q.
3. Divide both sides by 14: q = 2.

After the tax, the quantity drops to 2 crates.

• Quantity produced before tax: 8 crates.
• Quantity produced after tax: 2 crates.