Question

Suppose that a movie studio is deciding on the quality ξ of its next film. Anticipated revenues in $millions (from ticket sales, downloads, licensing to Netflix, etc) equal R(f)-10ξ + 5ξ2. more expensive to make better movies so costs are given by C()-6 * (f2 + 4). 2. It's a. Find the profit-maximizing quality b. How much money can the studio make if it chooses the optimal? c. Confirm that at the optimum MR MC, d. What fixed cost would make the studio indifferent between proceeding and canceling the project?

Answer 1

a)

Profit is given by

$\pi =R(\xi)-C(\xi)$

$\pi =10\xi+5\xi ^{2}-\left [ 6\xi ^{2}+24 \right ]$

$\pi =10\xi-\xi ^{2}-24$

To find maximum profit set

$\frac{d\pi }{d\xi }=0$

$10-2\xi=0$

$\xi=5$

Optimal quality is 5

b)

$\pi =10\xi-\xi ^{2}-24$

$Put\: \: \xi=5$

$\pi =10*5-5 ^{2}-24=1$

Firm can make $1 million in this project.

c)

$R(\xi )=10\xi +5\xi ^{2}$

$MR=dR(\xi )/d\xi =10+10\xi$

$Put\: \: \xi=5$

$MR=10+10*5=60$

$C(\xi )=6*(\xi ^{2}+4)$

$MC=dC(\xi )/d\xi =12\xi$

$Put\: \: \xi=5$

$MC=12\xi=12*6=60$

We can observe that MR=MC

d)

If additional fixed cost which is equal to profit is incurred, profit would be zero.

At this stage one would be indifferent between proceeding and cancelling the project.

Additional fixed cost=Optimal profit=1 million

$C(\xi )=6*(\xi ^{2}+4)$

We can see that firm is incurring a fixed cost of $24 million.

So, a fixed cost of $25 million will make the studio indifferent.