Prove that.....

(15) 1. a. Prove that the technology f (L, K) = L2 + K 2 exhibits increasing returns to scale. b. What is the formula for the average product of capital? c. For the total cost curve T C (q) = q3, prove the technology exhibits decreasing returns to scale. (5) 2. Draw typical average and marginal cost curves for a rm with an increasing returns to scale technology