A Monopolist Faces the Inverse Demand for Its Output

question 58

Essay

A monopolist faces the inverse demand for its output:
p = 30 - Q
The monopolist also has a constant marginal and average cost of $4/unit.The government is seeking ways to collect tax revenue from the monopolist and faces two proposals:
i.Impose a specific tax of t on the monopolist.
ii.Impose an ad valorem tax of a on the monopolist.
a.Suppose the government imposes a 20% ad valorem tax on the monopolist.What price and quantity does the monopolist choose and how much revenue does the government generate from the tax?
b.Rather than an ad valorem tax,what is the government's revenue from a specific tax of t imposed on the monopolist? Your answer should be in terms of t.
c.Show that a specific tax of $3.70/unit generates the same revenue as a 20% ad valorem tax (approximately).
d.Which tax has a greater distortion on the monopoly output?

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Definitions:

Hypotheses

Proposed explanations or predictions for a phenomenon, made as a starting point for further investigation.

Indirect Observations

Observations made through the use of instruments or tools rather than through direct sensory experience.

Replicable

Capable of being repeated or duplicated under similar conditions, allowing for verification of results.

Perfect Objectivity

An ideal state of being unbiased and impartial, free from personal feelings or opinions.