# Useyour knowledge about two-part pricing to advise the comp

Useyour knowledge about two-part pricing to advise the company below. A companyhas a bar and is trying to decide on the cover charge (if any) and price foreach drink. It has done a modest surveyin which it asked customers to classify themselves as light drinkers or heavydrinkers and to indicate the number of drinks they would typically consumeduring the evening.The estimate fromthe survey is that a change in the price equal to $1 per drink causes lightdrinkers to change their consumption on average by 0.5 drinks per night. However, a change in price of $1 causes heavydrinkers to change their consumption on average by 1.0 drink per night. For both groups a typical consumer will notconsume anything once the price reaches $9 per drink. (They may instead go toanother bar or not go to a bar at all.)Draw a demand curvefor a typical light drinker and for a typical heavy drinker on the samediagram. Explain your diagram. Write equations for the curves inslope-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 adownward-sloping demand curve, the slope will be a negative number.)If 300 people visitthe bar on a typical evening, with 200 people being light drinkers and 100people being heavy drinkers, draw an overall demand curve for all of theconsumers combined. (Figure out theintercept on the vertical axis; this intercept indicates the price at whichnobody would purchase anything. Alsodetermine the intercept on the horizontal axis; this intercept indicates whatthe total quantity demanded would be if the price of drinks were zero.)What is the slopeand what is the intercept for this demand curve? Write an equation in slope-intercept form.Recall that, in thecase of a straight-line demand curve, the slope of the marginal revenue linefor a company that does not practice price discrimination is double the slopeof the (total) market demand curve. If the marginal costof making drinks (the alcohol, the bartender’s labor, and the amortized cost ofpurchasing 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 fordrinks? How many drinks would be sold ona typical evening? What would yourprofits be? Show your work.If you cut your price by $1 per drink AND assess the maximumpossible cover charge without causing a typical light drinker to refuse toenter 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.