This is a 5 part question; (a-e)The question reads: Suppose that a market is described by the following supply & demand equations: Qs=2P & Qd=300-P
a) Solve for the equalibrium price & quantity. (I think I understand this process.)
b)Suppose that a tax of T is placed on buyers so the new demand equation is:
Qd=300-(P+T). Solve for new equalib. What happens to the price received by seller, the price paid by buyers, & qty sold?
c)Tax revenue is T x Q. Use your answer to part (b) to solve for tax revenue as a function of T.
d) Graph the DWL
e) Gov't levies a tax on good of $200/unit. Is this a good policy? Why/Why not? Can you propose a better policy?
a) set Qs=Qd and solve for P.
b) Same, set Qs=Qd and solve for P. Buyer pays P+T, seller gets P. (I get P=100-T/3)
c) Let P^ and Q^ be the equilibrium price and quantity. TR=T*Q^. From supply Q^=2P^. Substitute. TR=T*2P^ = T*2*(100-T/3)= 200T-2T^2/3
d) dwl is dead weight loss, and is represented by the little triangle below demand above supply and to the right of the equilibrium Q.
e) In general, whether a tax is a good policy or not depends on how it compares to the other policy choices. However, this $200 tax is a BAD policy because the government could raise the same amount of money with a lower tax rate. Use calculus on the equation from c) to find the revenue maximizing tax rate. TR' = 200 - 4T/3. You have a maxima at T=150.
a) To solve for the equilibrium price and quantity, we need to set the quantity supplied (Qs) equal to the quantity demanded (Qd) and solve for P.
Qs = 2P
Qd = 300 - P
Setting the two equations equal to each other:
2P = 300 - P
Combining like terms:
3P = 300
Dividing both sides by 3:
P = 100
Now that we have the equilibrium price (P), we can substitute it back into either the supply or demand equation to find the equilibrium quantity (Q).
Using the demand equation:
Qd = 300 - P
Qd = 300 - 100
Qd = 200
Therefore, the equilibrium price is $100 and the equilibrium quantity is 200 units.
b) If a tax (T) is placed on buyers, the new demand equation becomes:
Qd = 300 - (P + T)
To find the new equilibrium price and quantity, we set the new quantity demanded (Qd) equal to the quantity supplied (Qs) as before:
Qs = 2P
Qd = 300 - (P + T)
Setting the two equations equal to each other:
2P = 300 - (P + T)
Simplifying:
2P = 300 - P - T
Combining like terms:
3P = 300 - T
Dividing both sides by 3:
P = (300 - T) / 3
This equation represents the new equilibrium price. To find the new equilibrium quantity, substitute this value of P back into either the supply or demand equation.
Using the supply equation:
Qs = 2P
Qs = 2[(300 - T) / 3]
Qs = (600 - 2T) / 3
So, the new equilibrium price is (300 - T) / 3 and the new equilibrium quantity is (600 - 2T) / 3.
c) Tax revenue is calculated by multiplying the tax rate (T) by the quantity sold (Q). From part (b), we know that the quantity sold under the new equilibrium is (600 - 2T) / 3. Therefore, tax revenue can be expressed as:
Tax Revenue = T * Q
= T * [(600 - 2T) / 3]
= (600T - 2T^2) / 3
d) To graph the Deadweight Loss (DWL), we need to first understand what it represents. DWL is the loss in economic efficiency caused by the tax. It is represented by the triangle between the supply and demand curves, above the equilibrium quantity, and below the new equilibrium quantity.
To graph the DWL, plot the supply and demand curves on a graph, with quantity (Q) on the x-axis and price (P) on the y-axis. Identify the equilibrium price and quantity as found in part (a), and then plot the new equilibrium quantity and price found in part (b).
Next, draw a line connecting the new equilibrium price with the old equilibrium price. Draw another line connecting the new equilibrium quantity with the price at which supply equals demand under no tax (which can be found by substituting the old equilibrium price into the supply or demand equation). The area between these lines and above the equilibrium quantity represents the DWL.
e) Whether a $200/unit tax imposed by the government is a good policy depends on various factors, including the specific context and objectives. However, generally speaking, such a high tax can have significant implications.
Imposing a $200 tax per unit would likely lead to a shift in the demand curve, causing a decrease in quantity demanded and an increase in the price paid by buyers. The tax revenue would be substantial, given the high tax rate and assuming a significant quantity is still being sold.
However, such a high tax rate may also result in unintended consequences. It could lead to a decrease in producer surplus (price received by sellers) due to the increased burden of the tax. Additionally, it could lead to a decrease in consumer surplus (difference between the price paid and the maximum willingness to pay) as buyers have to pay a higher price.
A better policy alternative could be to consider a more moderate tax rate, which balances the tax revenue generated with the potential negative effects on producers and consumers. This would entail conducting a careful analysis of the market dynamics and considering the desired outcomes, such as revenue generation, efficiency, and equity.
a) To find the equilibrium price and quantity, we need to set the supply and demand equations equal to each other:
Qs = Qd
2P = 300 - P
Adding P to both sides:
3P = 300
Dividing by 3:
P = 100
Plugging the value of P back into the supply or demand equation:
Qs = 2P
Qs = 2(100)
Qs = 200
Therefore, the equilibrium price is $100 and the equilibrium quantity is 200.
b) With a tax of T on buyers, the new demand equation becomes:
Qd = 300 - (P + T)
To solve for the new equilibrium price and quantity, we set the new supply and demand equations equal to each other:
Qs = Qd
2P = 300 - (P + T)
Adding P + T to both sides:
3P + T = 300
Subtracting T from both sides:
3P = 300 - T
Dividing by 3:
P = (300 - T) / 3
Plugging the value of P back into the supply or demand equation:
Qs = 2P
Qs = 2[(300 - T) / 3]
Qs = (600 - 2T) / 3
Therefore, the new equilibrium price is (300 - T) / 3 and the new equilibrium quantity is (600 - 2T) / 3.
c) Tax revenue is calculated by multiplying the tax per unit (T) by the quantity sold (Q):
Tax Revenue = T x Q
Substituting the values from part (b):
Tax Revenue = T x [(600 - 2T) / 3]
d) To graph the Deadweight Loss (DWL), we need to compare the initial equilibrium quantity (200) and the new equilibrium quantity from part (b) [(600 - 2T) / 3]. The DWL is the area between the supply and demand curves, between the initial quantity (200) and the new equilibrium quantity.
e) To determine if a tax policy is good or not, we need to evaluate its impact on various factors. In this case, the government is levying a tax of $200 per unit. This would decrease the quantity sold and increase the price paid by buyers.
Whether this is a good policy or not depends on the specific goals and context of the government. Generally, a tax policy is meant to generate revenue for the government and potentially influence market behavior. However, it may also have unintended consequences, such as reducing consumer welfare, increasing production costs, or creating market inefficiencies.
To propose a better policy, it would be helpful to have more information about the specific goals of the government and the market dynamics. For example, the government could consider implementing a tax on sellers instead of buyers, adjusting the tax rate, or exploring alternative market interventions that align with their objectives.