Question

The representative firm has technology described by a linear production function Y=190N. Compared to the previous question, labor productivity decreased. The representative household has preferences over consumption and leisure represented by the following utility function u(c,ℓ)=c+18ℓ. At the equilibrium, how big is the labor input? At the equilibrium, how much output is produced?

Answer 1

The equilibrium labor input and output in the described scenario depend on the interaction between the linear production function and household utility function. Without additional details, such as wage rate and prices, the exact equilibrium cannot be determined.

Step-by-step explanation:

The presented scenario involves analyzing the equilibrium in a labor market where the production function is described as linear, specifically Y = 190N, indicating that the output (Y) is solely dependent on the amount of labor (N) used. The utility function given for the representative household, u(c,ℓ) = c + 18ℓ specifies preferences over consumption (c) and leisure (ℓ). In this model, the labor input and output produced at equilibrium are determined by the interaction between the production function and utility maximization by households.

However, given the information provided, it is not possible to calculate the exact value of the labor input or output produced at equilibrium without additional details about the wage rate, prices, and how the consumption and leisure choices interact with the production function. These elements are essential to solve for equilibrium labor input and output produced.