Suppose a market is characterized by a unionized and a non-unionized sector. Both sectors initially have supply given by Q=10,000+25w, and demand by Q=20,000-10w, where w is the weekly salary. Find the initial equilibrium wage and labor utilization. Now, in the unionized sector, a wage of 300 is negotiated. What is the demand and supply for labor in the unionized sector? Any surplus migrates to the uncovered sector. What is the new equilibrium wage and labor utilization in that sector?© BrainMass Inc. brainmass.com October 16, 2018, 9:11 pm ad1c9bdddf
For equilibrium, 20,000-10w = 10,000+25w
Or (25 + 10)w = 20,000 - 10,000
Or 35w = 10,000, which gives w = 10,000/35 = $285.71
At w = 285.71, the demand and supply is: Q = 20,000 - 10* 285.71 = 17,142.90
What is the new equilibrium wage and labor utilization in that sector?
Firm Costs and Response to Input Price Changes
For a firm facing a constant returns to scale Cobb-Douglas production, derive the total cost function for the firm, Calculate the elasticity of total cost with respect to output for the firm, and illustrate the effect of the increase in the wage on labor utilization
Question 2: Firm Costs and Response to Input Price Changes
Suppose a firm faces a constant returns to scale Cobb-Douglas production of the form:
2.1 Derive the total cost function for the firm, and calculate the total cost of producing 10,000 units of the output.
2.2 Calculate the elasticity of total cost with respect to output for the firm, and determine the percentage change in total costs if the firm sought to increase production by 5 percent.
2.3 Now, suppose the cost of labor rises from w = $100 to wnew = $400. Using isoquant-isocost analysis with labor on the horizontal axis and capital on the vertical analysis, illustrate the effect of the increase in the wage on labor utilization, carefully denoting both the input substitution and output effects of the wage increase. Discuss what factors determine the magnitude of the output effect. (NOTE: The firm faces a highly elastic (price-sensitive) demand curve in the product market.)
NOTE: Throughout the problem, assume a long-run analysis in which the firm can vary both the amount of labor and capital employed.View Full Posting Details