1. Rapinoe Ltd. Rapinoe Ltd. is London-based startup that is planning to produce rislets. Rapinoe just patented a novel technology. Its production function is y = Ak l', where A = 2, a = 1/4 and B = 1/2. The rislets market is very competitive. The ongoing price is p = $20. Benzema is facing a wage rate w = $6 and a rental rate of capital r = 0.01. Your job as unpaid intern is to figure out Rapinoe's optimal scale of production and estimate its profits at that scale. (a) Compute marginal product of capital and marginal product of labor. (5 points) (b) Compute and draw Rapinoe's long-run cost function. (10 points) (c) Compute and draw Rapinoe's long-run marginal cost function. (5 points) (d) Compute Rapinoe's optimal scale of production and profits. (10 points) (e) Rapinoe's CEO is concerned that his investors will be unhappy at such a low level of profit. He asks you for advice on how to increase profits. How do you answer? (5 points)