A monopolist is operating at an output level where (€) = 3. The government imposes a quantity tax of $6 per unit of output. If the demand curve facing the monopolist is linear, how much does the price rise?
The price will rise by $3. The quantity tax of $6 per unit of output will be passed on to the consumer, so the price will increase by half of the tax amount.
To find out how much the price rises after the imposition of the quantity tax, we need to understand the effects of the tax on the monopolist's cost and revenue, and then calculate the change in price.
1. Start by understanding the demand curve: The fact that the demand curve facing the monopolist is linear is helpful in determining the change in price. However, we would need specific information about the demand curve (slope and intercept) to calculate the change accurately. This information is not given in the question, so we'll proceed with a general explanation assuming a linear demand curve.
2. Determine the monopolist's initial output and price: The question provides that at the current output level, the price (€) is 3. Let's call this initial price P_initial.
3. Calculate the monopolist's revenue before the tax: Revenue (R) is calculated by multiplying the price (P_initial) by the quantity sold (Q_initial). Since the output level is not given, let's assume it as Q_initial for now: R_initial = P_initial * Q_initial.
4. Calculate the monopolist's cost: The cost to the monopolist is not provided in the question. To calculate the effect of the quantity tax, we don't need the actual cost figures. However, it's worth noting that the tax may affect the monopolist's cost structure, resulting in changes in production costs.
5. Determine the new quantity supplied after the tax: The quantity tax of $6 per unit of output raises the monopolist's cost. Let's call the new quantity supplied as Q_after_tax. So, Q_after_tax = Q_initial - 1.
6. Calculate the monopolist's new revenue after the tax: Now that we know the new quantity supplied, we can calculate the monopolist's new revenue (R_after_tax) by multiplying the new price (P_after_tax) by the quantity sold (Q_after_tax).
7. Calculate the new price after the tax: The new price after the tax can be calculated by dividing the new revenue (R_after_tax) by the new quantity (Q_after_tax). So, P_after_tax = R_after_tax / Q_after_tax.
8. Calculate the change in price: Finally, subtract the initial price (P_initial) from the new price after the tax (P_after_tax) to find the change in price.
Since specific values are missing from the question (such as the slope of the demand curve and the initial quantity), we cannot perform the calculations to provide an exact answer. However, by following these steps and applying specific values for the demand curve and initial quantity, you can find the exact change in price resulting from the quantity tax.
To determine how much the price rises when the government imposes a quantity tax, we need to calculate the difference between the price before and after the tax.
1. Start by finding the price before the tax (P_before). In this case, the price before the tax is €3.
2. Next, calculate the difference between the price before and after the tax (ΔP). This can be found by subtracting the price after the tax (P_after) from the price before the tax.
3. To find the price after the tax (P_after), we need to consider the impact of the tax on the monopolist's supply and demand. The quantity tax of $6 per unit of output increases the cost of production for the monopolist, leading to a shift in the supply curve. However, the demand curve remains unchanged.
4. Since the demand curve is linear, we can assume that the elasticity of demand remains constant. Therefore, the monopolist will pass on some portion of the tax to the consumers by raising the price.
5. The price after the tax can be found by adding the tax per unit of output (ΔQ) to the initial price before the tax. In this case, the tax per unit of output is $6.
To summarize:
P_before = €3
ΔQ = $6
P_after = P_before + ΔQ
Therefore, to find the price after the tax, we can substitute the values:
P_after = €3 + $6
By converting the currency to a common unit, such as euros or dollars, we can calculate the exact price rise.