The Simple Model of Production Consider an economy with the following Cobb-Douglas production function: Y = Aralf 0 < a. B <1 Further, assume the assumptions made in lecture 1 hold, i.e., this economy follows a standard Simple Model of Production model. Answer the following questions. a) For what values of a and does the production function assume constant returns to scale? Show vour work. b) Prove that Y = wL + rK if constant returns to scale hold. What assumptions did you have to make about the competitive nature of the capital and labour markets? Discuss the economic intuition of this formula. O Assume A =1,K=25.L=100and a=B=0.5. Would firms be tempted to change their current demand for capital if the real rental rate was equal to 7? Explain. d) Derive the demand for labour in this economy. Whatwould be the equilibrium wage?