Use your knowledge about two-part pricing to
advise the company below.
A company has a bar and is trying to decide on the cover
charge (if any) and price for each drink.
It has done a modest survey in which it asked customers to classify
themselves as light drinkers or heavy drinkers and to indicate the number of
drinks they would typically consume during the evening.
The estimate from
the survey is that a change in the price equal to $1 per drink causes light
drinkers to change their consumption on average by 0.5 drinks per night. However, a change in price of $1 causes heavy
drinkers to change their consumption on average by 1.0 drink per night. For both groups a typical consumer will not
consume anything once the price reaches $9 per drink. (They may instead go to
another bar or not go to a bar at all.)
Draw a demand curve
for a typical light drinker and for a typical heavy drinker on the same
diagram. Explain your diagram. Write equations for the curves in
slope-intercept form. The general form for such an equation is P = a + bQ,
where P is the price for the drinks, Q is the quantity of drinks purchased, ‘a’
is the intercept on the vertical axis, and ’b’ is the slope. (In the case of a
downward-sloping demand curve, the slope will be a negative number.)
If 300 people visit
the bar on a typical evening, with 200 people being light drinkers and 100
people being heavy drinkers, draw an overall demand curve for all of the
consumers combined. (Figure out the
intercept on the vertical axis; this intercept indicates the price at which
nobody would purchase anything. Also
determine the intercept on the horizontal axis; this intercept indicates what
the total quantity demanded would be if the price of drinks were zero.)
What is the slope
and what is the intercept for this demand curve? Write an equation in slope-intercept form.
Recall that, in the
case of a straight-line demand curve, the slope of the marginal revenue line
for a company that does not practice price discrimination is double the slope
of the (total) market demand curve.
If the marginal cost
of making drinks (the alcohol, the bartender’s labor, and the amortized cost of
purchasing glasses and cleaning them repeatedly) is constant at $5 per drink,
and if no cover charge is assessed, what is the best price to charge for
drinks? How many drinks would be sold on
a typical evening? What would your
profits be? Show your work.
If you cut your price by $1 per drink AND assess the maximum
possible cover charge without causing a typical light drinker to refuse to
enter the bar, would your profits improve?
How high would the cover charge be?
Calculate both the cover charge and your total profits. Would the new pricing increase profits? Explain your answer fully.