Apple produces iPhones using capital and labor according to the production function

Q^S= (1/64)K^0.75L^0.5

where Q^Sis annual production, K is the annual number of hours of capital used and L is the annual number of hours of labor used.

Labor's hourly wage is $40 and capital's hourly rental rate is $240.

As it turns out, based on these facts, the marginal cost (MC) of producing an iPhone is as follows:

MC = 5120/(Q^0.2).(The S superscript is omitted, but the Q here is supply.)

This is the marginal costequationas it depends on Q.Notice that MC falls when Q rises because iPhone production has increasing returns to scale (RTS) in production.RTS = 1.25 (the sum of the exponents 0.75 and.50).So, production has economies of scale (EOS) of 0.8.With this cost structure in production, Apple can satisfy the entire market demand for iPhones, and it has a monopoly in iPhone production and sales.

The demand curve Apple faces for iPhones is

Q^D= 960,000 - 600P

where P is the iPhone's price.

1. Determine the iPhone's total revenueequation(PQ) as it depends on Q.(Leave off the D superscript on Q but remember that this Q is demand.)

PQ = _________________.

2. Determine the iPhone's marginal revenue (MR)equationas it depends on Q.

MR = _________________.

3. Determine the profit-maximizing number of iPhones to make annually.(Using "goal seek" in an Excel spreadsheet is the easiest way to do this.)

Q = ______________.

4. What is the marginal cost of making an iPhone at this quantity?

MC = _____________.

5. What is the marginal revenue of making an iPhone at this quantity?

MR = _____________.

Because the production function is of this form (Cobb-Douglas), the optimal amount of money for Apple to spend on labor (WL) will always be 2/3 of that spent on capital (RK).[2/3 is .50/.75 ... the ratio of the exponents on labor and capital].Given that W =$40 and R = $240, this means that L = 4K is always optimal for Apple.Substituting 4K for L into the production function, gives us back total output Q = (1/32)K^1.25.Now, using the Q you got in #3 above, what is K?

6. K = _______________.

What is L?

7. L = _______________.

What is total cost C (which equals WL + RK)?

8. C = _______________.

What is the average cost of producing an iPhone?

9. AC = _______________.

What is the price of an iPhone?

10. P = ______________.

What is the total revenue from iPhone sales (PQ)?

11. PQ = ____________________.

Whatis Apple's profit from iPhone sales?

12. Profit = ________________________.

What share of Apple's revenues from selling iPhones is profit?

13. Profit per unit =_____________ percent?[Answer to one decimal, i.e., XX.X]

How much is the markup of an iPhone above its marginal cost?

14. P - MC = ____________.

What is the Lerner Index for the iPhone market at the profit-maximizing Q?

15. Lerner Index = _____________.[Answer to two decimals, i.e., X.XX]

What is the choke demand price of an iPhone?

16. Choke P = _____________.

What is Apple's producer surplus from making iPhones?

17. Producer surplus = ____________________.

What is the consumer surplus from buying iPhones?

18. Consumer surplus = ___________________.