Northern Lumber operates a large lumber-processing mill in a small town in Washington State. It is one of the larger lumber producers in the region and has some market power in the sale of that product. A recent consulting study has indicated that the price elasticity of demand for the firm's product is about -3.0. Also, Northern is the dominant employer in the local labor market, and effectively can be considered as a monopsonist in the purchase of labor. The firm's labor demand (i.e. marginal revenue product) function is;
MRP = 1 000 - 2L
where L is the number of workers. Because of its size relative to the labor supply in the area, Northern faces an upward sloping labor supply function,
w = 50 + 0.025L and ME = 50 + 0.050L
where w is the daily wage rate and ME is the marginal expenditure on labor.
Once the firm determines the optimal rate of labor input and the wage rate, the rate of output is determined. The firm uses a cost-plus pricing formula that includes the price elasticity of demand as a determinant in setting product price. The same study indicated that average cost is about RM300 per unit (1 000 board feet) of lumber.
Requirements
1. Determine the amount of labor that the firm should employ in order to maximize profit.
2. Determine the wage rate the firm will have to pay.
3. What price will the firm charge per unit of output?