×

Inverse Demand curve with Macroeconomics Assignment Solution

September 20, 2023
Robert Howell
Robert Howell
🇬🇧 United Kingdom
Macroeconomics
Renowned as Robert Howell, hailing from Imperial College London, UK, with 15 years' experience and a Ph.D., excels as a Macroeconomics Homework Consultant, delivering unparalleled academic guidance.
Key Topics
  • Calculate Equilibrium and Demand Curve

Calculate Equilibrium and Demand Curve

There are n = 25 restaurants in a downtown area open for lunch. Each one has a monopoly on their specific cuisine (there is only one Italian, only one Mexican, only one Japanese, and so on for twenty-five different unique gastronomic alternatives). However, there is high substitutability from a customer's perspective, as diners like a variety depending on taste and, of course, prices. Restaurant I faces the following individual demand: Di(pi) = (1000/n) - pi. The cost function for restaurant I is C(xi) = xi^2 + 50.

  1. What is the inverse demand curve that restaurant faces? What is the marginal revenue MRI and the marginal cost MCI?
  2. How many customers xi will the restaurant I serve, and what price pi will it advertise?
  3. How much profit will the restaurant make? Since all other restaurants have the same demand and costs as restaurant I, is having in this downtown profitable? With low barriers to entry how many new restaurants will open? As n increases, Di(Pi) falls until it is tangent to AC. Find equilibrium n for which profits are zero.
  4. Starting from the long-run equilibrium n you found in part c, the cost of leases now increases, and the new cost function that each restaurant faces becomes C(Xi)=Xi^2 + 200. What is the new equilibrium number of firms in the market?

Solution:

a)

Qi=1000/25-pi=40-pi

Pi=40-Qi{ inverse demand}

MRi=40-2qi

MCi=∆TC/∆Q=2qi

b)

Firm Profit Maximizing quantity is at MRi=MCi

40-2qi=2qi

40=4qi

Qi=40)4=10

Pi=40-10=30

c)

πi = pi*xi – xi ^2 – 50

we have : xi = 10 and pi = 30,

then πi = 150

Yes it’s profitable because πi<0

ACi = C(xi) / xi = xi + 50 /xi

Min (ACi) :

∆ACi/∆xi = 0 ↔ 1 – 50/(xi^2) = 0 ↔ xi = √50

Pi = ACi↔ 1000/n - xi = xi + 50 /xi

↔ 1000/n = 2* xi + 50 /xi = 3*√50

↔n = 1000/ (3*√50)

↔ n = 47

d)

ACi = C(xi) / xi = xi + 200 /xi

Min (ACi) :

∆ACi/∆xi = 0 ↔ 1 – 200/(xi^2) = 0 ↔ xi = √200

Pi = ACi↔ 1000/n - xi = xi + 200 /xi

↔ 1000/n = 2* xi + 200 /xi = 3*√200

↔ n = 1000/ (3*√200)

↔ n = 24

Related Samples

Explore our comprehensive collection of sample materials designed specifically for students studying macroeconomics. These resources provide a diverse range of practical examples illustrating key macroeconomic principles, evaluations of market trends, examinations of aggregate consumer behavior, and strategic frameworks for decision-making. Immerse yourself in these samples to acquire valuable perspectives on the complex dynamics of macroeconomic theory and its real-world implications.