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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

QG

= 0

QC

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)

=4,500,000,000

(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:

P=.

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

P=30,833.33

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?

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(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.

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