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A restaurant/bar is analyzing its pricing of beer. It has determined that the price elasticity of demand for beer is 0.8; the cross-price elasticity for wine concerning the price of beer is 0.9; the cross-price elasticity for appetizers is -1.4, and the cross-price elasticity for entrees is -2.2. The current average price of a beer at this bar is $4.50, and the restaurant sells 250 pints of beer a night. The price of wine averages $8 a glass, and on a typical night, 40 glasses of wine are purchased. An appetizer is priced at an average price of $6, and an entree costs $12 on average. The average number of appetizers and entrees sold per night is 70 and 25, respectively. The marginal cost of a pint of beer is $2; an additional glass of wine sold increases costs by $5; an appetizer increase costs by $4, and an entree has a marginal cost of $7. The restaurant is considering lowering the price of beer to $4.

1. What is the restaurant's profit (before the price change)?

2. Using the midpoint formula (described at the top of page 73--use the midpoint instead of the initial point in calculating the per cent change), by what per cent would the price of beer change?

3. Using the price elasticity of demand, the approximation for the per cent change in the price of a beer you just calculated, and the equation at the start of section 6.5, how many pints of beer would the restaurant sell after the price change?

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Insha Fatima
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28 Sep 2019

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Related questions

Scenario 1 A cupcake store is located in a mall and is the only cupcake store in that mall. The demand schedule for cupcakes (per dozen) is given in the table below. If the marginal cost to produce a dozen cupcakes is $4 per unit, how many units should the firm produce? Price Quantity Purchased (Dozen per day) $12 3 $11 7 $10 12 $9 20 $8 35 $7 60 $6 100 $5 160 $4 250

1. What price should the cupcake store charge?

2. If the fixed cost for the firm is $100 per day, how much profit will the firm make in one day?

3. What is the price elasticity of demand at the optimal price/quantity combination (use the next lower price level as the second point in your calculation)?

4. Is the formula for finding the correct level of output on the bottom of page 65 in your text satisfied?


Scenario 2 A restaurant/bar is analyzing its pricing of beer. It has determined that the price elasticity of demand for beer is 0.8, the cross-price elasticity for wine with respect to the price of beer is 0.9, the cross-price elasticity for appetizers is -1.4 and the cross-price elasticity for entrees is -2.2. The current average price of a beer at this bar is $4.50 and the restaurant sells 250 pints of beer a night. The price of wine averages $8 a glass and in a typical night 40 glasses of wine are purchased. An appetizer is priced at an average price of $6 and an entree costs $12 on average. The average number of appetizers and entrees sold per night is 70 and 25, respectively. The marginal cost of a pint of beer is $2, an additional glass of wine sold increases costs by $5, an appetizer increases costs by $4 and an entree has a marginal cost of $7. The restaurant is considering lowering the price of beer to $4.

1. What is the restaurant's profit (prior to the price change)?

2. Using the midpoint formula at the bottom of page 64, by what percent would the price of beer change? Using the price elasticity of demand and the approximation for the change in quantity on page 67, how many pints of beer would the restaurant sell after the price change?

3. Using the price change of beer and the cross-price elasticities, how many glasses of wine, appetizers, and entrees would the restaurant sell after the price change of beer?

4. What would the profit of the restaurant be after the price change?

5. Should the restaurant lower the price of beer to $4 based on your analysis?


Scenario 3 In "Kitchen Nightmares", Chef Gordon Ramsa visits struggling restaurants and gives the owners of the restaurant a number of recommendations intended to reverse the restaurant's prospects. One suggestion Chef Ramsay commonly makes is to reduce the size of the restaurant's menu and concentrate on a smaller number of offerings. Our textbook has several theories that can be used to explain how that recommendation can reduce costs.

1. Explain how the recommendation is an application of Economies and Diseconomies of Scope.

2. Explain how the Learning Curve concept also would suggest a smaller menu would lead to a cost reduction.



In 1981, a Boston-based gas station owner set the highest gasoline prices in the nation. During that summer, he charged $1.69 per gallon for unleaded gas during the daytime and $2.59 per gallon at night, when other downtown gas stations were closed. His all-time high price was $3.99. Even at these extreme prices, however, the station owner sold an average of 3,000 gallons per week, half of this at night. Despite catcalls, pickets, and even vandalism from angry motorists during the gasoline crisis, the owner "stuck by his pumps"; he even charged $1 for air. As he put it, "People think of gas stations as public mammary glands, but they're wrong. This is a business, and it's important to generate profits from every part of it. If I can use a resource, like air, to pay for the electric bill, so much the better. If you allow capitalism in its true form, it works beautifully".

The station owner was an avowed profit maximizer, albeit not a very attractive one. How did he profit from his dual-price policy? The answer is price discrimination. Although his costs varied little day and night, the elasticity of demand varied greatly. He maximized his profit by charging a higher price at night when demand is much more inelastic than during the day. In fact, we could go so far as to say that he operated under different market structures, day and night. At night, he appeared to have a pure local monopoly. Motorists desperate for gas had to drive miles to find another station open during those hours. Thus, the owner sold gas even at gouging prices. At those prices, the motorist may have preferred to buy five gallons rather than a full tank. During the day, he faced many competitors within blocks and numerous stations in neighboring Cambridge. That is, the market resembled monopolistic competition. There was some product differentiation due to locational convenience and brand allegiance. Nonetheless, in normal times excess profits are limited by the relatively free entry of new firms. (The gasoline crisis and accompanying supply shortage afforded sellers short-run, excess profits.)

A. Suppose that, during the day, the station owner's demand is given by PD = 2.06 - .00025QD. The marginal cost of selling gasoline is $1.31 per gallon. At his current $1.69 price, he sells 1,500 gallons per week. Is this price-output combination optimal? Explain.

B. The station owner sells an equal number of gallons at night, setting PN = $2.59. Suppose elasticity of demand is EP = -3. According to the optimal markup rule, is this price profit-maximizing?

Use your knowledge about price-searching firms and 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 regression study 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 regression study 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 the price of $1 causes heavy drinkers to change their consumption on average by 1.0 drinks 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.

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. What is the slope and what is the intercept for this demand curve? Write an equation in slope-intercept form. 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? 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 profit?

Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal to total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, plus 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.) You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every Q that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually, you can solve for the exact best P, Q, and cover charge.

Review of the slope-intercept form: Y= a - bX; a = the intercept on the Y-axis and b = the absolute value of the slope (slope=(change in Y)/(change in X)) For a demand curve: P=a-b Q. The intercept on the vertical axis would indicate a price that is so high that the quantity demanded becomes zero. The slope is the ratio of a change in price divided by the change in quantity demanded; the extra credit problem gives you information to determine the slope for a light drinker and the slope for a heavy drinker.

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