Asked by Mitchell Allen on Jun 06, 2024
Verified
Xavier and Yvette are the only two persons on a desert island.There are only two goods, nuts and berries.Xavier's utility function is U(Nx, Bx) NxBx.Yvette's utility function is U(Ny, By) 2Ny By.Xavier is endowed with 5 units of berries and 13 units of nuts.Yvette is endowed with 6 units of berries and 8 units of nuts.In a competitive equilibrium for this economy, how many units of berries does Xavier consume?
A) 13.50
B) 18.50
C) 15.50
D) 31
E) None of the above.
Utility Function
A mathematical representation in economics that captures the level of satisfaction or utility that consumers derive from consuming goods and services.
Desert Island
A secluded and uninhabited island, often used in scenarios and thought experiments in economics and ethics to explore human behavior in isolation.
Competitive Equilibrium
A market situation where supply equates demand, leaving no incentive for price changes, assuming all agents are price-takers.
- Grasp the concept of utility functions and how they influence consumer choice decisions.
- Gain insight into the core tenets of competitive equilibrium and how they pertain to pricing mechanisms in simple exchange economies.
Verified Answer
ZK
Zybrea KnightJun 07, 2024
Final Answer :
C
Explanation :
To find the competitive equilibrium, we need to solve for the prices of nuts and berries. Let the price of berries be P and the price of nuts be 1. Then we have the following optimization problems for Xavier and Yvette:
Max U(Nx, Bx) subject to P(Nx) + 1(Bx) ≤ 13 and P(Bx) + 1(Nx) ≤ 5
Max U(Ny, By) subject to P(Ny) + 1(By) ≤ 8 and P(By) + 1(Ny) ≤ 6
Solving these problems, we get:
Nx = 7, Bx = 6.5, P = 2/13, Ny = 2.5, By = 6, P = 2/8
Therefore, Xavier consumes 6.5 units of berries.
Max U(Nx, Bx) subject to P(Nx) + 1(Bx) ≤ 13 and P(Bx) + 1(Nx) ≤ 5
Max U(Ny, By) subject to P(Ny) + 1(By) ≤ 8 and P(By) + 1(Ny) ≤ 6
Solving these problems, we get:
Nx = 7, Bx = 6.5, P = 2/13, Ny = 2.5, By = 6, P = 2/8
Therefore, Xavier consumes 6.5 units of berries.
Learning Objectives
- Grasp the concept of utility functions and how they influence consumer choice decisions.
- Gain insight into the core tenets of competitive equilibrium and how they pertain to pricing mechanisms in simple exchange economies.