(Short-run Cost Minimization) Rosenberg produces boardgames using Labour(L) and Machines(K) as inputs. His board game production function is given as follows: Q = f(K; L) = 15K^3/4 + L^1/2 At the end of last year Rosenberg and only machine for $2, 000. After using this bough this first machine for 5 years it will lose all its value. Rosenberg calculates depreciation linearly (depreciation will be 20% a year in this case). There is no other use for this machine and it will have no value after the five years are up. Rosenberg is not able to buy any more machines at this moment.
(a) What type of returns to scale (increasing/constant/decreasing) does Rosenberg’s production function exhibit? (5 marks)
(b) If Rosenberg’s production function exhibits increasing returns to scale how could it be transformed to decreasing returns to scale? If it exhibits constant returns to scale how could it be transformed to increasing returns to scale? If it exhibits decreasing returns to scale how can it be transformed to constant returns to scale? (5 marks)
(c) What is Rosenberg’s annual fixed cost of production? Is the fixed cost sunk or not? Explain your answer. (5 marks)
(d) Rosenberg pays a wage equal to 3. What is Rosenberg’s annual total cost function? (5marks)