Question 1: Consider the labor market model we saw in class. Final output in the economy is produced using capital K and labor L. The production function is: Y = K3X4L1'4 + KL Assume the supply of all inputs are exogenous and equal to E and K. Perfectly competitive rms are price-takers and choose how much capital and labor to demand by maximizing prots. Let w and r denote the wage and rental rate of one unit of labor and capital respectively. (a) Is this production function increasing, decreasing or constant returns to scale? Briey explain why. (7 marks) (b) Derive the optimal hiring condition for capital. Explain why the marginal product of capital is decreasing in K. (15 marks) (Note: You do not need to tidy up the math, you can leave the condition as is.)