A film studio in Hollywood produces movies according to the function (yes, they can also produce fractions of movies… Think of half a movie as a B-movie or so.) q = F(K, L) = K0.5L 0.5 /100 (reads as K to the power of 0.5 times L to the power of 0.5 divided by 100). In the short run, capital (studios, gear) is fixed at a level of 100. It costs $4,000 to rent a unit of capital and $1,000 to hire a unit of labor (actors, stuntmen, camera crew etc.) The Hollywood studio is doing its planning for the next year and can choose capital and labor.
(a) What is the isocost line for a budget of $4 million? What is the equation of the isoquant? Find the slope of the isoquant and the isocost line.2 What condition has to hold so that you minimize costs? Derive the minimized costs as a function of output. How many movies can you afford to produce at the afore-mentioned budget?
(b) What is the additional cost of an additional movie now? How much does it cost on average to produce a movie? Does it depend on the number of movies you are producing? What is the relationship to the returns to scale of the production function?
(c) Comparing these costs to the situation when you have 100 units of capital, then is your average cost higher or lower [assuming you want to produce 10 movies]? What about the marginal cost? Briefly state why.
(d) Imagine that you come in as a new manager and discover that the current capital-labor ratio is K/L = 1. If you spend 10,000 additional (small fractions of) dollars on hiring more labor, how many additional (small) units of labor can you hire and how much more output can you produce? Answer the same for capital. If you had to stay on the same budget, would you hire or fire workers, in order to maximize output?
(e) Still assume that the current capital-labor ratio is K/L = 1. How many (small) units of capital can you save when you hire four additional (small) units of labor, holding output constant? How much money can you save when you do so?
