Final answer:
The per-unit tax that maximizes the government's tax yield is $0. The maximum amount of tax yield the government can collect is $0. After the introduction of the per-unit tax, the suppliers will be willing to sell their product at the new price of $60.
Step-by-step explanation:
To find the per-unit tax that maximizes the government's tax yield, we need to determine the equilibrium quantity and price after the tax is introduced.
(a) First, let us set the demand and supply functions equal to each other and solve for the equilibrium quantity (q).
Demand: p = 180−8q
Supply: p = 25+2q
Setting the two equations equal gives us: 180−8q = 25+2q
Simplifying, we get: 10q = 155
Solving for q, we find: q = 15.5.
Now, substitute the value of q back into the demand or supply function to find the equilibrium price (p).
Using the demand function, we have: p = 180−8(15.5) = 60.
Therefore, the equilibrium quantity is 15.5 units and the equilibrium price is $60.
To find the per-unit tax that maximizes the government's tax yield, we need to calculate the tax revenue at various tax rates. Let t represent the tax rate (per unit).
The tax revenue is given by: Tax Revenue = t x Quantity Sold.
Substituting the values, we get: Tax Revenue = t x 15.5.
Maximizing the tax revenue implies maximizing the tax rate.
The maximum tax rate will occur when the quantity sold is zero.
Therefore, the maximum per-unit tax rate that maximizes the government's tax yield is $0.
(b) The maximum amount of tax yield that the government can collect is the tax revenue when the tax rate is maximized. Using the tax revenue formula, we have: Tax Yield = t x Quantity Sold. Substituting the values, we get: Tax Yield = 0 x 15.5 = $0.
(c) After the introduction of the per-unit tax, suppliers will adjust their selling price to cover the additional cost of the tax. In this case, the new price that suppliers will be willing to sell their product at can be calculated by adding the per-unit tax to the equilibrium price. Using the tax rate of 0 and the equilibrium price of $60, the new price will be: New Price = $60 + $0 = $60.