Hi k9queen!
These are the answers to your questions:
a) The formulas for the total revenue, total cost and profit are quite
easy:
Total revenue = (price)*(quantity demanded)
Total cost = (cost per unit)*(quantity demanded) + fixed costs
Profit = Total revenue - Total Cost
We know the price and quantity from the table you give above. The
costs per book are constant at $10, while the fixed cost to the
publisher are $2,000,000 (he must pay this sum to the author
independetly of how many books he sells). Therefore, the revenue costs
and profits for each quantity are:
price quantity Revenue Cost Profit
$100 0 0 2000000 -2000000
90 100,000 9000000 3000000 6000000
80 200,000 16000000 4000000 12000000
70 300,000 21000000 5000000 16000000
60 400,000 24000000 6000000 18000000
50 500,000 25000000 7000000 18000000
40 600,000 24000000 8000000 16000000
30 700,000 21000000 9000000 12000000
20 800,000 16000000 10000000 6000000
10 900,000 9000000 11000000 -2000000
0 1,000,000 0 12000000 -12000000
Clearly, a profit-maximizer publisher should sell either 400,000 or
500,000 books, at a price of either $60 or $50 respectively. These are
the quantities and prices that maximize the profits, at $18,000,000.
Other quantities result in a smaller profit.
b) The definition of marginal revenue and how to calculate it can be
found in the following link:
Marginal Revenue
http://ingrimayne.saintjoe.edu/econ/elasticity/RevEtDemand.html
As you can see, it's the change in revenue from selling an extra unit.
This would be the marginal revenue at each price:
price quantity Revenue Marginal Revenue
$100 0 0 ---
90 100,000 9000000 (9000000-0)/(100000-0)=90
80 200,000 16000000 (16m - 9m)/(200k-100k)=70
70 300,000 21000000 (21m -16m)/(300k-200k)=50
60 400,000 24000000 30
50 500,000 25000000 10
40 600,000 24000000 -10
30 700,000 21000000 -30
20 800,000 16000000 -50
10 900,000 9000000 -70
0 1,000,000 0 -90
As you can see, as price decreases, marginal revenue decreases. An
explanation to this can be found in the link I provided above: the
idea is that as price decreases, even though the publisher's sales
increase (because more people buy the book), he must also sell all the
other books at a lower price than before, thus obtaining a lower
revenue.
c) Marginal costs are obtained in a similar fashion as marginal
revenues. In this case, since the cost per book, this is easy: the
marginal cost is $10. That is, producing an additional book adds $10
to the total cost. Notice that the marginal cost is completely
independent of the 2,000,000 of fixed costs of the publisher. Knowing
this, we know have all the information we need for the graph. You can
find the graph at
http://www.angelfire.com/alt/elmarto
As you can see (also from the marginal revenue table), the marginal
revenue and marginal cost are equal at 500,000 books (in the table,
the MR of 500000 is 10, and the marginal cost is always 10). This
means that the publisher must sell this quanity.
Why is this so? Consider what happens if he already paid the author
and he hasn't printed any books yet. He's considering printing the
first 100,000 books. Is this profitable? Yes, because the Marginal
Revenue (MR) is greater than the marginal cost (MC); i.e., each
additional book earns him more money than the cost of producing it. So
he prints the first 100,000 books. He's now considering producing
another 100,000. It turns out that this also profitable: the MR at
200,000 is $70, while the MC is $10. Using the same reasoning, the
publisher must continue adding books until the MR equals the MC.
Beyond that point, since the MR is decreasing, more books will cost
more than the MR. Therefore, it's not profitable to sell them. Thus he
sells 500,000 books at $50 each.
d) Why is the shaded are a deadweight loss? The publisher is selling
his books at $50. However, producing them costs only $10. The
"society" (reflected in the demand curve) would be willing to buy more
books if the price were lower. Moreover, it would be socially
efficient to produce more books; because the society values the books
more than the cost of producing them. For example, the demand price at
600,000 books is $40, therefore, it would be more socially efficient
to produce this quantity, because the society values each book at $40,
while the cost of producing each is $10.
Nonetheless, this does not go on forever. Consider what happens if the
publisher sells 1,000,000 books. The society values each at $0 (too
many books :-) ), but the cost of production is $10 each. Therefore,
it's not efficient to produce 1,000,000. Clearly, the socially
efficient quantity of books is that which makes the demand price equal
to the marginal cost. Beyond there, it's inefficient to add more
books, because society values these extra books less than the cost of
producing them.
So, let's get to the deadweight loss: it would be efficient to produce
all those books between 500,000 and 900,000. However, since the
publisher sets the price (it has a monopoly - he's the only one who
can sell the book) he will not sell 900,000 (we've already seen that
the profit is maximized at 500,000). Therefore, the value of all the
books between 500,000 and 900,000 are a "deadweight loss" to society,
goods that would be efficient to produce but aren't being produced.
The graphic can also be found at the previous link.
e) It would not affect it. Recall that the publishers sets the
quantity of books such that the MR equals the MC. Recall also that the
MC has nothing to do with what the publisher pays to the author (and
it obviously has nothing to do with the revenue). Therefore, the
quantity that maximizes profits is still 500,000, no matter what the
publisher pays the author. This is related to the definition of "sunk
costs"
Sunk Cost
http://www.internettime.com/blog/archives/000099.html
f) This has partially been answered in d). We have seen that
maximizing economic efficiency would lead the publisher to set the
quantity so that the demand price equals the MC. This happens at
900,00 books (demand price: $10). However, at this price and quantity
(although it is economically efficient) the publisher suffers severe
losses. Check the table in question 1: at 900,000 books, the publisher
looses $2,000,000.
Google search strategy:
marginal revenue
marginal cost
sunk cost
I hope this helps! If you have any doubt regarding my answer, please
request a clarification before rating it. Otherwise I await your
rating and final comments.
Best wishes!
elmarto |
