1 l. The following functi on describes the dem and condition for a company that makes caps
featuring names of college and professi on al teams in a variety of sports.
Q = 2,000 - lOOP
where Qis cap sales and Pis price .
a. How many caps could be sold at $12 each?
b. What should the price be in or der for the company to sell 1,000 caps?
c. At what price would cap sales equal zero ?
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(!) The follo~ ng relations describe monthly demand and supply for a computer supp ort service
catenng to small businesses.
QD = 3,000 - l0P
Qs = -1,000 + l0P
where Qi s the number of busines ses that need services and Pis the monthly fee, in dollars.
a. At wh at average monthly fee would demand equal zero?
b . At what average monthly fee would supply equal zero?
c. Plot th e suppl y and demand curves.
d . Wh at is the equilibrium price / output level?
e. Suppose demand increases and leads to a new demand curve:
QD = 3,500 - I0P
Wh at is the effect on supply? What are the new equilibrium P and Q?
f. Suppo se new suppliers enter the market due to the increase in demand so the new supply
curve is Q = -500 + 1 O P. What are the new equilibrium price and equilibrium quanti ty?
Show these changes on the graph.
---~--- =- :-,-;-,---------------
he ABC marketing consulting firm found that a particular brand of tablet PCs has the
following demand curve for a certain region:
Q = 10,000 - 200P + 0.03Pop + 0.61 + 0.2A
where Qis the quantity per month, Pis price ($), Pop is population, /is disposable in come
per household (S), and A is advertising expenditure ($).
a. Determine the demand curve for the company in a market in which P= 300,
Pop= 1,000,000, I = 30,000, and A= 15,000.
b. Calculate the quantity demanded at prices of $200, $175, $150, and $125.
c. Calculate the rice necessa to sell 45,000 units.
13-} Backgro u nd In form ation: Restaurants have traditionally used bottom-end wines to sell by
t----/ the glass (BTG) at reasonably low prices per glass. In recent years, there has been a growing
trend with in the resta urant industry to extend BTG programs to higher-end wines. In doing
so, they have grea tly expanded the sales of higher-end wines. The typical markup on a bottle
of wine is 100 perce nt or mor e, meaning that a bottle ofwine that sells at retail for $25 in a
wine shop can be pric ed at $100 in a restaurant. To simplify this discussion, suppose that wine
is offered at $10 per glass. The size of the serving can be adjusted depending on the price
per bo ttle of the wine being poured. For example , a 4-ounce pour can be offered for wines in
the $40 to $50 range anda 2-ounce pour can be offered for wines in the $80 to $100 range.
Beca use a bottle has 25.4 ounces, both examples provide more revenue from BTG sales than
from full-bottle sales! Such programs have been quite successful and produce little loss due
to un sold wine in the bottle because , with proper storage , a partial bottle can be poured the
n ext evening with no notable change in taste.
The Problem: Suppose you manage a restaurant with a BTG program. You sell 200 glasses
p er week at $10 per glass. Asan experiment, you once raised the price during the week to
$11 a glass and found that you sold 20 glasses less than before the price change. Suppose you
assume this information as the basis for a full demand curve for wine BTG at your restaurant.
a Obtain an algebraic and graphical depiction ofyour restaurant's BTG demand .
. How man y glasses do you expect to sell at $15 per glass?
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