The Inverse Demand for Tacos Is Given by P =

question 105

Essay

The inverse demand for tacos is given by P = 10 - 0.02Q, where P is the price per taco and Q is the total number of tacos brought to market. There are two taco shops in the local market. Shop 1's cost function is given by C₁ = 0.01q₁², where q₁ is the number of tacos it brings to market. Shop 2's cost function is given by C₂ = 0.01q₂², where q₂ is the number of tacos it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. Let Q = q₁ + q₂.
a. What is shop 1's profit function?
b. What is shop 2's profit function?

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Definitions:

Market Price

The current price at which an asset or service can be bought or sold in an open and competitive market.

Gross Profit Percentage

A financial ratio expressing gross profit as a percentage of revenue, indicating the efficiency of production or service delivery.

Net Profit Margin Percentage

This is a financial metric that represents the percentage of revenue that remains as profit after all operating expenses, interest, taxes, and preferred stock dividends have been deducted from a company's total revenue.

Cost of Goods Sold Percentage

A ratio that compares the cost of goods sold to the total sales revenue, indicating the efficiency of production and pricing.