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

Q^S = 1024K^0.8L^0.4

where Q^S is production, K is the amount of capital used and L is the amount of labor used.

Labor's annual cost per worker is $32,768 and capital's cost per unit is $2,097,152. As it turns out, based on these facts, the marginal cost (MC) of prEach year, Apple produces iPhones using capital and labor according to the production function

Q^S = 1024K^0.8L^0.4

where Q^S is production, K is the amount of capital used and L is the amount of labor used.

Labor's annual cost per worker is $32,768 and capital's cost per unit is $2,097,152. As it turns out, based on these facts, the marginal cost (MC) of producing an iPhone is as follows:

MC = 2560/Q^(1/6). (The S superscript is omitted, but the Q here is supply.)

The demand curve Apple faces for iPhones is

Q^D = 1,000,000 - 1000P

where P is the iPhone's price.

1. Determine the iPhone's total revenue equation (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) equation as it depends on Q.

MR = ____________________________________.

3. Determine the profit-maximizing number of iPhones to make. (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 = ____________.oducing an iPhone is as follows:

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 50 percent of that spent on capital (RK). [0.50 is (0.4) divided by (0.8) ... the ratio of the exponents on labor and capital, /]. In short, we know that WL = (0.5)(RK) is always optimal for Apple. With a bit of math, it is possible to show that this implies the following relationship between Q and L when Apple is producing optimally:

Q = 64L^1.2.

Now, using this relationship and the Q you got in #3 above, what is L?

6. L = ______________.