I keep getting two different answers for the first part (10000/w and 40000/w) but I don't know which one is correct **Problem Description**Consider an economy with a production function given by $ Y = AK^{0.5}L^{0.5} $ where $ A $ is the total factor productivity (TFP), $ K $ is the capital stock and $ L $ is the labor input. For simplicity, assume capital is fixed and equal to 1. Assume $ A=200 $.a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage.b. Assume labor supply is inelastic and fixed at $ \bar{L} = 100 $. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.c. Suppose the economy faces a negative productivity shock and TFP is now $ A=100 $. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage?**Graph Descriptions**b. The graph will include:- **Labor Demand Curve:** Plot showing the relationship between real wage and quantity of labor demanded. It slopes downward, indicating that as wages decrease, more labor is demanded.- **Labor Supply Curve:** A vertical line at $ \bar{L} = 100 $, indicating fixed labor supply regardless of the wage.c. In the event of a negative productivity shock:- The **new labor demand curve** will be less steep than before, reflecting the decrease in productivity. It will still slope downward.Each axis will be labeled appropriately, with the quantity of labor on the horizontal axis and real wage on the vertical axis. Equilibrium points should be marked to show the values of employment and real wage before and after the productivity shock.

Production function : Y = A K0.5L0.5 Where , A = 200 Optimal labor demand is at the point where…

Consider an economy with production function given by Y = AK0.5 10.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=200. a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage. b. Assume labor supply is inelastic and fixed at L = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.

Consider an economy with production function given by Y = AK0.5 10.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=200. a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage. b. Assume labor supply is inelastic and fixed at L = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

I keep getting two different answers for the first part (10000/w and 40000/w) but I don't know which one is correct

**Problem Description**

Consider an economy with a production function given by $ Y = AK^{0.5}L^{0.5} $ where $ A $ is the total factor productivity (TFP), $ K $ is the capital stock and $ L $ is the labor input. For simplicity, assume capital is fixed and equal to 1. Assume $ A=200 $.

a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage.

b. Assume labor supply is inelastic and fixed at $ \bar{L} = 100 $. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph.

c. Suppose the economy faces a negative productivity shock and TFP is now $ A=100 $. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage?

**Graph Descriptions**

b. The graph will include:

- **Labor Demand Curve:** Plot showing the relationship between real wage and quantity of labor demanded. It slopes downward, indicating that as wages decrease, more labor is demanded.
- **Labor Supply Curve:** A vertical line at $ \bar{L} = 100 $, indicating fixed labor supply regardless of the wage.

c. In the event of a negative productivity shock:

- The **new labor demand curve** will be less steep than before, reflecting the decrease in productivity. It will still slope downward.

Each axis will be labeled appropriately, with the quantity of labor on the horizontal axis and real wage on the vertical axis. Equilibrium points should be marked to show the values of employment and real wage before and after the productivity shock.

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