View the step-by-step solution to:

Due tomorrow morning.

I am stuck on part C of the attached question! Please help!! Due tomorrow morning.

1.  (40 points) Suppose that Perfect Labs produces autoclaves (laboratory equipment) at a constant marginal cost equal to $20,000 and a fixed cost of $10 billion. Perfect Labs sells its autoclaves in Canada and in Germany. You are trying to determine the best pricing strategy for Perfect Labs and you know that the demands in each country are the following:

QG = 4, 000, 000 100PG           and    QC = 1, 000, 000 20PC

where subscript G denotes Germany and subscript C denotes Canada.

(a) (10 points) What is the quantity of autoclaves that Perfect Labs will sell in each market and at what price(s)? What is the total profit?

Inverse demands are:

PG = 40,000 -

Pc = 50,000 -


Profits are : π = TR − TC = (QG PG + QC PC)− (20,000Q + 10,000,000,000).

π = TR − TC = ((4, 000, 000 100PG) (40,000 - )) + ((1, 000, 000 20PC)( 50,000 - ))− (20,000QC+ 20,000QG + 10,000,000,000)

Differentiate and set each derivative to zero to determine the profit- maximizing quantities:

= 0


= 0



Now we can plug this back into the demand curves to get price:

1,000,000 = 4,000,000 − 100PG

PG= $30,000

300,000 = 1,000,000 − 20PC

PC= $35,000


Now put everything into the profit equation:

π = TR − TC

= ((4, 000, 000 - 100(30,000) (40,000 - )) + ((1, 000, 000 - 20(35,000))( 50,000 - ))− (20,000(1,300,000)) + 10,000,000,000)

= (1,000,000)(30,000) + (300,000)(35,000)− (36,000,000,000)


(b) (10 points) If Canada and Germany sign a trade agreement which forces Perfect Labs to charge the same price in both markets, how many units will be sold in each market and at what price? What is the firm's total profit in that case?

If we have to charge the same amount in each country, then we substitute Q=QG+QC. This gives us a new total demand curve of:

Q=5,000,000 - 120P and an inverse demand curve of P=.

Since this is linear we can say the MR curve has the same intercept and twice the slope:



Marginal cost is the derivative if TC, so:

= 20,000


Profits-maximizing quantities are when MR=MC. So:

20,000 = .

Q= 1,300,000


Plug this back in to find price:

1,300,000=5,000,000 - 120P



Now we can take this price and put it back into the demand curves for each market to see how much will be bought in each county.

PG = 40,000 -

30,833.33= 40,000 -

QG= 916,667

Pc = 50,000 -

30,833.33= 50,000 -

QC= 383,333

This means total profit would be:

π = TR − TC

π = (1,300,000*30,833.33)- (20,000(1,300,000) +10,000,000,000)

π = $4,083,329,000


(c) (10 points) Now suppose that Perfect Labs considers charging a two-part tariff in each country. What is the profit-maximizing fixed fee and per unit price in each country? What is the total profit for Perfect Labs in this case?

(d) (3 points) If Perfect Labs were able to employ perfect price discrimination, what would be its total profit? Explain.

(e) (1 points) If Perfect Labs could choose, which of the three pricing strategies (a)-(c) would it choose? Why?

(f) (6 points) If consumers were allowed to vote for one of those three pricing strategies (a)-(c), which one would they vote for? Explain.

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.


Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question