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3. (20 marks) Consider a representative firm that faces a constant returns to scale produc- tion function Y = zF(K, N), where Y is output of consumption goods, z is TFP, K is physical capital, and No is labour input. The amount of capital is assumed to be given and fixed. The production function exhibits a positive marginal product of labour, as well as diminishing returns to labour. The firm seeks to maximize profits. Suppose that the government imposes an output tax Ty 0 units of the consumption good for each unit of labour the firm hires. Show the joint effect of these taxes on the firm's profit maximization problem, optimality condition, and demand for labor, using both equations and graphs. For a given wage rate, what will be the effect on average labour productivity