Maximizing Output with Wage Taxation: A Production Function Example

The actual wage is equal to the marginal output because the worker is paid based on the additional output they produce. In other words, the wage is determined by the marginal contribution of each worker to the production process.\n\nTo find the output per day, we need to maximize the production function Y = 500N - 0.4N^2 with respect to the number of workers N. Taking the derivative of the production function with respect to N and setting it equal to zero, we can find the value of N that maximizes the output:\n\ndY/dN = 500 - 0.8N = 0\n=> N = 500/0.8 = 625\n\nSubstituting N = 625 back into the production function, we can find the output per day:\n\nY = 500N - 0.4N^2\nY = 500(625) - 0.4(625)^2\nY = 312,500 - 156,250 = 156,250\n\nTherefore, the output per day is 156,250 units.