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.

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