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

Q^S= 128K^0.75L^0.50

Where Qs is the quantity produced, and K and L are the capital and labor used in production. Labor's annual cost per worker is $36,000 and capital's annual cost per unit is $3,456,000. As it turns out, based on these facts, the marginal cost (MC) of producing an iPhone is as follows

MC = 18,000/(Q^0.20). *The superscript S is omitted but the Q means supply!

Average cost of producing an iPhone is AC = 22,500/(Q^0.20)

These are the marginal and average cost equations as they depend on Q. Notice that MC and Ac fall when Q rises because iPhone production has increasing returns to scale (RTS) in production. RTS= 1.25 = 5/4,(the sum of the exponents 3/4and 2/4= 5/4). So, production has economies of scale (EOS) of 4/5= 1/(5/4))

The demand curve Apple faces for IPhones is

Q^D= 65,000,000 - 50,000P where P is the iPhone's price.

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

2. Determine the profit-maximizing number of iPhones to make. You will get a fractional number, but round it off to

the closest whole number that minimizes MR-MC (drop the decimals in Q)

Q = _________________

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

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

Because of Cobb-Douglas, Q = 1024K^(5/4), which can be rewritten as K= (Q^0.80)/256

Now, using this relationship and the Q you got in Question 3 above, what is K(to the nearest tenth)?

5. K= ____________

6. Since you now know W, R, and K, what is L(to the nearest tenth)?

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

8. What is the average cost of producing an iPhone to the nearest penny?

9. What is the price of producing an iPhone?

10. What is Apple's total revenue from iPhone sales (PQ)?

11. What is Apple's profit from iPhone sales to the nearest dollar?

12. Profit per unit to one decimal = ___________ percent?

13. How large is the markup of an iPhone above its marginal cost?

P - MC = _______

14. What is the iPhone's price as a multiple of its average production cost to two decimals?

P = __________ AC.[This should look like P = (X.XX)AC.]

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

16. What is the price elasticity of demand for the iPhone (E_D) at this price and quantity?

17. Choke P= _____________ .

Given this choke price and Apple's average cost of making an iPhone, what is the minimum number of iPhones Apple must produce in order to get the average cost of an iPhone down below the choke price? Call this number Qmin and round up to the nearest whole number.

18. Qmin= _______________

19. How many iPhones does Apple have to make in order to finally make a profit?

Q*min= _______________

20. What is Apple's producer surplus from making iPhones?

21. What is the consumer surplus from buying iPhones?