Equilibrium Price and Quantity

To find the equilibrium price and quantity, we’ll set the demand and supply equations equal to each other:

Demand (Qd) = Supply (Qs)

8000 – 200P = 50P – 1000

Now, let’s solve for P:

8000 + 1000 = 50P + 200P

9000 = 250P

P = 9000 / 250

P = 36

So, the equilibrium price (P) is $36,000.

Now, plug this price back into either the demand or supply equation to find the equilibrium quantity (Q):

Qd = 8000 – 200P Qd = 8000 – 200 * 36 Qd = 8000 – 7200 Qd = 800

The equilibrium quantity (Q) is 800 motorcycles per year.

Now, let’s create a diagram to visualize this equilibrium:

Consumer Surplus: To calculate consumer surplus, we need to find the area of the triangle above the price line and below the demand curve.

Consumer Surplus = 0.5 * (36 – 0) * (800 – 0) = $14,400

Producer Surplus: To calculate producer surplus, we need to find the area of the triangle below the price line and above the supply curve.

Producer Surplus = 0.5 * (36 – 0) * (800 – 0) = $14,400

Total Surplus: Total surplus is the sum of consumer and producer surplus.

Total Surplus = $14,400 (Consumer Surplus) + $14,400 (Producer Surplus) = $28,800

Part B: Imposing a Tax

The government wants to reduce the number of traditional combustion engine motorcycles to 500 per year. To achieve this, we can calculate the specific (per unit) tax needed:

Tax per unit = (Previous Equilibrium Quantity – Desired Quantity) / Previous Equilibrium Quantity Tax per unit = (800 – 500) / 800 Tax per unit = 300 / 800 Tax per unit = 0.375

Now, let’s calculate the total tax burden on consumers and sellers. Since the tax is per unit, it will be applied to each motorcycle sold.

Total Tax Burden on Consumers = Tax per unit * Desired Quantity Total Tax Burden on Consumers = 0.375 * 500 = $187.50 (thousands)

Total Tax Burden on Sellers = Tax per unit * Desired Quantity Total Tax Burden on Sellers = 0.375 * 500 = $187.50 (thousands)

Now, let’s create a new diagram to show the effects of the tax:

Consumer Surplus (after tax): To calculate consumer surplus, we need to find the area between the demand curve (new) and the price line (including the tax).

Consumer Surplus (after tax) = 0.5 * (36 – 30) * (500 – 0) = $1,500

Producer Surplus (after tax): To calculate producer surplus, we need to find the area between the supply curve (new) and the price line (net of tax).

Producer Surplus (after tax) = 0.5 * (30 – 0) * (500 – 0) = $7,500

Part C: Effects of the Tax

According to the model of supply and demand, society is worse off as a result of the tax imposed by the government in part ‘b’.

Before the tax, the total surplus was $28,800, with consumer surplus and producer surplus both at $14,400. After the tax, the total surplus has decreased to $9,000 ($1,500 consumer surplus + $7,500 producer surplus).

The tax has led to a significant loss in total surplus, indicating that resources are not allocated as efficiently as before. This loss in surplus represents deadweight loss, which reflects the inefficiency introduced by the tax. Additionally, the burden of the tax falls on both consumers and producers, making them worse off. Consumers pay more for motorcycles, and producers receive less revenue.

In summary, the tax intended to encourage the adoption of electric motorcycles has reduced overall welfare and made society worse off due to the inefficiencies introduced in the market.