Consider a Competitive Firm with the Short-Run Cost Function

question 26

Essay

Consider a competitive firm with the short-run cost function
C(q)= 20 + 6q + 5q²
The firm faces a market price of p for its output.
a.Derive the firm's profit maximizing condition.Is the sufficient second order condition satisfied?
b.Suppose a specific tax of t (t < p)is levied on only this firm in the industry.What is the profit maximizing level of output as a function of p and t? (Assume the price is high enough that the firm does not shut down)
c.How does the output change as the tax increases? Use calculus to determine the relevant comparative static.
d.How does the firm's profit chance as the tax increases? Again,use calculus to determine the relevant comparative static.Show that profit decreases as t increases.

---

Definitions:

Ionic Compound

An ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding, typically formed between metal cations and non-metal anions.

Phosphorus

A reactive, non-metallic element found in Group 15 of the periodic table, essential for life.

Calcium

A chemical element with the symbol Ca and atomic number 20, a reactive, pale yellow metal that forms compounds with many other elements.

Ionic Formula

A notation that represents the composition of an ionic compound by showing the ratio of ions present in the compound.