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) = K^0.5L^ 0.5 /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.

in long run:

The same Hollywood studio is doing its planning for the next year and can choose capital and labor. (a) What are all the different combinations of capital and labour that you can aord on a budget of $4 million? If you hire one more worker (one more small unit of labour), how much capital can you afford less? (3) (b) What are all the different combinations of capital and labour that allow you to produce 9' movies? If you hire one more worker (one more small unit of labour), how many (small) units of capital can you let go and still produce the same output? (3) (c) What condition has to hold so that you minimize costs? Derive the minimized costs as a function of output. How many movies can you aord to produce at the aforementioned budget? (4) (d) What is the additional cost of an additional movie now? How much does it cost on average to produce a movie? (2) (e) Comparing these costs to the situation when you have 100 units of capital as in question 2, then is your average cost higher or lower [assuming you want to produce 10 movies]? What about the marginal cost? Briey state why. (2) (f) 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. Tf you had to stay on the same budget, would you hire or re workers, in order to maximize output? (2) (g) 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? (2)