Hello, Can you help me?
A film studio in Hollywood produces movies according to the function (assume studios can also produce fractions of movies…think of half a movie as a B-movie or so.)
q = F (K, L) = (2/100)K0.5L0.5.
In the short run, capital (studios, gear) is fixed at a level of 100. It costs $40 (in thousands) to rent a unit of capital and $10 (in thousands) to hire a unit of labor (actors, stuntmen, camera crew etc.).
(a) What is the fixed cost? What is the variable cost as a function of output q?1 (2)1Hint: You know what K is. From the production function, you can now determine what L has to be as a function
of output q. Once you know what L(q) is, it should be easy to find variable cost.
What is the marginal cost (MC) and the average cost (AC) of a movie? What is the average variable cost and average fixed cost? (2)
Where do the average and marginal cost curves intersect? What is the derivative of the AC curve and what value does it take at the intersection? What does it tell you about minimum average cost? (2)
Long-run costs (8 points, 2 Bonus Points)
The same 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 $16 million? What is the equation for the isoquant? Find the slope (the derivative) of this isoquant and this isocost line.2 What condition has to hold so that you minimize costs? The minimized cost as a function of output q is C(q) = 2000q (where Cost is in thousands of $), so how many movies can you afford to produce at the afore-mentioned budget? (4)
- (b) What is the additional cost of an additional movie now? How much does it cost on average to produce a movie? (2)
- (c) 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 8 movies]? What about the marginal cost? Briefly state why. (2)
- (d) Bonus Question: Imagine that you come in as a new manager and discover that the current capital-labor ratio is K/L = 1. If you spend 100 additional (marginal) dollars on hiring more labor, how many additional (marginal) units of labor can you hire and how much more output can you produce? Answer the same for capital. If you have to stay on the same budget, would you hire or fire workers?