Problem 1 Consider a firm which produces according to the following production function: q= A(√E+√K) = 2√E where q denotes output, E denotes the number of workers hired by the firm, K denotes capital, and A > 0 is some technology parameter. The marginal product of labor is therefore given by MPE In the short run, the firm rents 100 units of capital, at a rental cost of r 10 dollars per unit. The firm sells its output at a market price of 3 dollars, and has to pay each employee a wage of 15 dollars. The current factory setup implies that the technology parameter A = 20. == 1.1. In the short run, how many employees should the firm hire? How many units of output does the firm produce, and how much profit does it make? Show your work and make sure to verify all conditions for optimality. 1.2. Now suppose the firm can install a new technology which would streamline the production facility, and increase the technology parameter to A = 30, such that the new production function would become q= 30(√E+√K) If the firm would install this new technology, how would the optimal labor de- mand and output change? Assume all the other parameters (w, p, r, Ko) remain unchanged. 1.3. Suppose that the new technology described in Problem 1.2 costs 200 dollars to implement and operate. Should the firm invest in the new technology or not? Explain. 1.4. What is the short-run elasticity of labor demand (E) with respect to the wage rate (w)? Is the firm's labor demand elastic or inelastic?