Question

A monopolist produces a good at a constant marginal cost of 5 dollars. It sells that good in two separate cities, labeled 1 and 2 . Their demand curve for city 1 is q₁ =55−p₁ (or, equivalently, p₁ =55−q). The demand curve for city 2 is q₂ =70−2p₂ (or, equivalently, p₂ =35− 21q₂). First suppose it's impossible to travel between cities (for example, gas is extremely expensive). The monopolist therefore treats both markets separately, choosing p₁ in, city 1 and ν₁ in city 2 .

What is the optimal quantity produced in each city?

Answer 1

The optimal quantity produced in city 1 is 27.5 and the optimal quantity produced in city 2 is 23.75.

In the given scenario, the monopolist faces two distinct demand functions for the goods in City 1 and City 2, each characterized by different price and quantity relationships.

In City 1, the demand function is represented by q1=55−p1 , where p1 is the price and q1 is the quantity demanded.

The monopolist has determined that the optimal price (p1) to maximize profit is 27.5.

At this price, the corresponding optimal quantity (q1 ) that should be produced is also 27.5 units.

This indicates that, in City 1, the monopolist should supply 27.5 units of the good to meet the demand and maximize profit.

Moving on to City 2, the demand function is =70−2
`P_(2)`, with an optimal price (p2 ) determined to be 22.5.

At this price, the corresponding optimal quantity (q 2 ) is found to be 23.75 units.

Therefore, in City 2, the monopolist should produce and supply 23.75 units of the good to optimize profit.

Consequently, the monopolist's production strategy involves manufacturing 27.5 units for City 1 and 23.75 units for City 2.

This strategy is based on the analysis of the demand functions and the corresponding optimal prices and quantities in each city, aligning with the goal of maximizing overall profit in a monopolistic setting.

By tailoring production to the specific demand characteristics of each city, the monopolist aims to achieve an optimal balance between supply and demand, thereby maximizing its economic outcomes.