5. Suppose a firm manufactures a good with labor as the only input. Its production function is Q = L, where Q is output and L is total labor input employed. Suppose further that the firm is a monopolist in the product market and a monopsonist in the labor market. Workers may be male (M) or female (F); thus, L = LM + Lp.Let the inverse demand function for output and the supply functions for gender-specific labor be respectively p = A - ; Li = w, > 0; where p is the price received per unit of the good and w; is the wage the firm pays to each unit of labor of gender i, i e {M, F}.Let EMEF = 1. Suppose, in equilibrium, the firm is observed to hire both M and F workers, but pay M workers double the wage rate that it pays F workers. (a) Derive the exact numerical value of the elasticity of supply of male labor. [10 marks] (b) What happens to total male labor income as a proportion of total labor income when the output demand parameter A increases? Prove your claim. [10 marks ]