Problem B: The Production Model Consider the production model that we have seen in class with a production function for final output specified as Y = K1/413/4. Capital and labor available in the economy are, respectively, K = 40 and L = 50. B.1 Write down the profits maximization problem for firms in the production model (you can write profits in units of final output). Derive the first order conditions for the firm's maximization problem and provide the economic interpretation of the first order condition for labor. B.2 Please define the property of "Constant Returns to Scale" as we did in class. Does the production function above exhibit constant returns to scale? Show your computations. B.3 State the equations that constitute the competitive general equilibrium for the economy in the production model above. What are the variables that you need to solve for to obtain a solution to the equilibrium? B.4 What is the value of output, the rental rate of capital and the wage rate in equilibrium? Show your computations B.5 Suppose that the total labor available in the economy decreases to L = 40. In the new equilibrium, what is the change, if any, in the equilibrium wage rate compared to the equilibrium value you solved above? Show your computations and provide an economic explanation of your result using the diagram of the labor market that we have studied in class