ECO 6301 VII J

ECO 6301, Economics for Managers 1

Course Learning Outcomes for Unit VI At the end of this unit, you should be able to:

4. Evaluate strategic pricing decisions. 4.2 Describe the different types of auctions and the benefits of each.

7. Explain the implications of uncertainty in managerial decision-making.

7.2 Illustrate how to use expected value calculations to deal with uncertainty. Required Unit Resources Chapter 17: Making Decisions with Uncertainty (ULO 7.2) Chapter 18: Auctions (ULO 4.2) Article: Auctions versus Negotiations: The Effects of Inefficient Renegotiation (ULO 4.2) This article reinforces the concepts of auctions and negotiations. Unit Lesson Lesson: Uncertainty and Auctions (ULOs 4.2, 7.2) This lesson introduces you to the topics covered in this unit.

Expected Value Examples in economics often assume a certain level of knowledge about the market, but this is often not the case. Firms often face uncertainty in their decisions. Firms can use expected value to deal with uncertainty. Expected value takes the probability of certain outcomes to arrive at a weighted average outcome. This concept is best illustrated with an example. Assume there are two possible outcomes for a game, such as flipping a coin. The outcome of heads is likely to occur 50% of the time. If heads occurs, you win $1. The outcome of tails is likely to occur 50% of the time. If tails occurs, you lose $1. What is the expected value of this game? We can determine this by simply multiplying the payout by the probability that payout will occur and then summing the products for each outcome. E[X] = ph * xh + pt * xt where X is the payout of the game, p is the probability, x is the payout for a particular outcome and the subscripts h and t stand for heads and tails, respectively. In the example described: E[X] = 0.5 * $1 + 0.5 * $1 = $1 The expected value of the game is $1. You can imagine this simple example could be considerably complex with different outcomes and multiple probabilities to match. Obviously, a very important part of calculating expected value is to get the probabilities right. Decision-makers should be aware that their probabilities are likely not correct. A good way to handle this is to run multiple scenarios with different probabilities. A growing opportunity for firms is to use data analysis to model probabilities. When using data, however, firms need to be conscious of selection bias. Selection bias occurs when there is some difference in the data used

UNIT VI STUDY GUIDE Uncertainty and Auctions

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in the model probabilities that is not present in the target population. For a simple example of this, consider exit polls at elections. Pollsters survey voters coming out of voting booths to see how they voted and then make predictions on how the election will turn out based on those surveys. What happens, though, if pollsters primarily go to urban polling places to survey voters and do not go to rural polling places? If urban and rural voters vote the same way, this is not a problem, but if there are fundamental differences between how urban voters vote and how rural voters vote, then the surveys will be inaccurate. The surveys will likely be an accurate representation of how urban voters vote but not how voting is cast as a whole. Imagine a company making a similar mistake when marketing a new product. Uncertainty can never be completely eliminated, but firms can take steps to try to make informed decisions and minimize potential damage from unexpected events occurring.

Auctions You are probably most familiar with online auctions from websites like eBay. You might have gone to an antique auction when you were younger (possibly dragged there by a parent or grandparent). If you live near ranchers, you might have gone to a cattle auction. You have probably seen auctions portrayed on TV. You might have seen a silent auction at a charity. When sellers are unsure of the market value for their product, they can use auctions to make their sales. Auctions allow customers to bid for the product and thus reveal their value. Auctions help sellers sell their product and gain more information about the demand for their product. As seen from the previous paragraph, auctions can take a variety of forms. Auctions are often portrayed with somebody standing in front a room talking quickly and people in the audience bidding quickly. These are called oral auctions or English auctions. In these auctions, people make successive, increasing bids until only one bidder remains. The last remaining bidder gets the item at the last price they bid. So ultimately, the price is set marginally above the value of the second highest bidder (that is, a small amount above the value the second highest bidder holds). A few points about oral auctions are listed below.

1. First, the greater losing bids there are in an auction, the higher the winning bid amount will be. This point should make sense. The price will still go no higher than the highest valued bidder, but if the closer other bidders are to valuing the product similar to the highest valued bidder, the higher the winning bid will have to be.

2. Second, the more bidders there are in an auction, the more likely there will be other high valued bidders. On eBay, for example, ten-day auctions return 42% higher prices than three-day auctions as more time attracts more bidders (Froeb et al., 2018).

3. Third, there is an important piece of information that is never disclosed in an oral auction: What is the value the highest bidder holds for the product? All sellers know from an oral auction is that somebody valued the product more than the product sold for.

An auction that addresses this problem is a second-price auction, also called a Vickery auction. Second-price auctions are sealed-bid auctions, as opposed to the very public oral auction. There are also not multiple rounds of the auction where bidders can outbid the last bid. This is a type of sealed-bid auction where bidders submit a bid without knowing the other bids. The product is still awarded to the highest bidder, as in the oral auction, but rather than paying their bid, they pay the second-highest bid. A second-price auction encourages bidders to bid more aggressively and closer to their actual value (in fact the optimal strategy is to bid exactly their value) for the good since they know they will not have to pay their value, they will pay the bid of the second highest bidder. The outcome of the second-price auction is the same as the oral auction (the ultimate price is equal to, or just above, the value of the second-highest bid), but there are several benefits with a second-price auction that are not present with an oral auction.

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1. First, as mentioned, bidders are encouraged to bid more aggressively. This aggressive bidding will likely result in a higher price bid by the bidder with the second highest value. To see this, imagine an oral auction where the second-highest value bidder infers from the highest-value bidder that they will not be able to outbid the highest value bidder. The second-highest bidder might stop bidding early knowing it is futile. Leaving the bidding early results in a lower ultimate price for the seller.

2. Second, second-price auctions can be conducted from anywhere and bidders do not have to be present. Second-price auctions were popular with stamp dealers as far back as the 19th century (Froeb et al., 2018). Saving bidders the cost of travel (both explicit and opportunity) increases the net value for the product to the bidders, which can also increase bids.

3. Third, and addressing the information shortcoming discussed with oral auctions, second-price auctions give the seller information on the maximum value for their product since people, including the winning bidder, will bid their maximum value.

Now, reading about a second-price auction might lead to the question, “Well, why not do everything with a second-price auction but make the highest bidder pay the price they bid?” The problem with this approach is that bidders are actually incentivized not to bid their maximum value. Since the winning bidder ultimately has to pay their bid, they don’t want to pay their maximum value. If they did, they would be left with no profit (that is, the difference between their value and what they pay) and bidders are technically indifferent between winning and losing the auction. That means that bidders have an incentive to shade their bid. The seller would not get accurate information on bidders’ value and would potentially get a lower price as all bidders shade their bids.

Collusion and Irrational Behavior Auctions can lead to attempts at collusion, called bid rigging. In bid rigging, a group of bidders work together to keep down bids so that somebody from the group wins the auction at a bid lower than it otherwise would have been. Bid rigging is more likely to occur in smaller, frequent auctions. The smaller size increases the likelihood of communication between bidders and the frequency gives more opportunity to refine the rigging and punish members of the group that attempt to cheat. Collusion is also more likely in oral auctions than sealed-bid auctions, giving another benefit to second-price auctions over oral auctions. Finally, bid rigging is more likely when the winner of an auction is identified. If bidders can win in secret, there is an incentive to cheat (recall game theory from Unit IV). Auctions can sometimes lead to irrational behavior. This irrational behavior is particularly true in oral auctions where the desire to win overtakes the actual desire for the product being bid on. Oral auctions, more than sealed-bid auctions, are likely to suffer from over bidding. For producers, though, this can mean a higher winning bid. Bidding more than the value for the product can lead to the winner’s curse, where the winner of an auction is actually worse off for having won the auction.

References Froeb, L. M., McCann, B. T., Shor, M., & Ward, M. R. (2018). Managerial economics: A problem solving

approach (5th ed.) [Vital Source Bookshelf version]. https://online.vitalsource.com/#/books/9781337468015

Herweg, F., & Schmidt, K. M. (2017). Auctions versus negotiations: The effects of inefficient renegotiation.

RAND Journal of Economics, 48(3), 647–672. https://libraryresources.columbiasouthern.edu/login?url=http://search.ebscohost.com/login.aspx?direc t=true&db=bsu&AN=124623600&site=ehost-live&scope=site

ECO 6301, Economics for Managers 4

UNIT x STUDY GUIDE Title

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

In order to check your understanding of concepts covered in this unit, complete the Unit VI Check For Understanding activity. Unit VI Activity Alternate Format PDF NOTE: Be sure to maximize your internet browser so that no part of the presentation gets cut off.

ECO 6301, Economics for Managers 1

Course Learning Outcomes for Unit V At the end of this unit, you should be able to:

3. Analyze how price and output influence profit maximization under different market structures. 3.2 Explain how market power affects different types of pricing strategies.

4. Evaluate strategic pricing decisions.

4.1 Explain the conditions necessary to price discriminate. Required Unit Resources Chapter 12: More Realistic and Complex Pricing (ULO 3.2) Chapter 13: Direct Price Discrimination (ULO 4.1) Chapter 14: Indirect Price Discrimination (ULO 4.1) Article: Public Subsidies and the Location and Pricing of Sports This article discusses sports subsidies and pricing by analyzing how sports teams make decisions. Unit Lesson Lesson: Pricing and Greater Profit (ULOs 3.2, 4.1) This lesson introduces you to the topics covered in this unit. Firms have to answer two important questions: How much of their product should they produce, and how much should they charge for their product? The two are certainly linked, but the pricing decision is generally more complicated and drives the production decision. In basic economics, price is determined by the intersection of supply and demand, with price (P) determined on output determined by marginal revenue (MR) equals marginal cost (MC). A pricing strategy given earlier in the course is to set price such that the following equation holds:

In practice, however, pricing strategies often deviate from this standard theory. Sometimes, for example, firms have multiple products and this affects their pricing strategies. A firm might want to lower prices to sell more of a product, but if the increase in sales in one product simply comes from “stealing” sales from another of their products, then this is not really a net gain to the company. Also, owning more brands in a market gives the firm more market power, which means raising prices is more profitable. A potential problem with raising prices based on newfound market power is that it could attract the attention of the Antitrust Division of the Justice Department. The question is what to do strategically. A profit improving approach would be to raise the price on whichever product has a lower profit margin. With the lower margin product now being relatively more expensive, consumers will be more likely to purchase the higher profit margin. The preceding strategy is based on the goods being substitutes. If a single producer yields two products that are complements, then the profit maximizing action is to reduce the price on both products. By reducing the

UNIT V STUDY GUIDE Pricing and Greater Profit

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price, the producer increases quantity demanded for one good, but as a result, increases demand for the other good. Increasing sales of both products increases total profit. Another pricing situation of interest is when producers have fixed capacity (think a cruise ship or concert). In these cases, lowering prices to sell more product does not necessarily work because there might not be the ability to provide more product. The result might be a situation where MR > MC, contrary to the standard profit maximizing rule that MR = MC. Promotional pricing is another instance where firms might deviate from the standard pricing rule. Advertising can serve two broad goals: promote based on price or promote based on quality. The type of advertising will determine the appropriate price strategy. If the advertising focuses on promoting products based on price, demand will become more elastic, so lowering price makes sense. If the advertising focuses on promoting product quality, the demand will become more inelastic so raising price makes sense. This second point is important because price can often convey information about product quality. Promoting product quality and lowering price can send conflicting messages to consumers. Following in a similar vein of consumers inferring information about a product based on price, consumers sometimes have price expectations. Managing price expectations is why businesses will sometimes set a “suggested retail price” and then give the price of the product they are selling. The goal is to set a high price in the customer’s mind so that they will be happy about the lower price. You might also see producers set a low price but end up selling at a higher price or generating revenue some other way. Musicians might set low concert prices but then hold back tickets to sell themselves on the secondary market. Sports teams might set low prices to build up a fan base but then leverage that popularity to receive government subsidies for stadiums. If you would like to learn more about sports subsidies and pricing, you can read the article “Public Subsidies and the Location and Pricing of Sports” by Porter and Thomas.

Price Discrimination Up until now, the assumption has been that firms can only charge one price to all of their customers, but sometimes firms can charge different prices to different customers. This is called price discrimination. Examples of price discrimination are matinee ticket prices for movies and discounts for seniors and military members. Several criteria must be met for firms to successfully price discriminate. There must be consumers with different elasticities, that is different price sensitivity, and firms must be able to identify those different customers (consumers with more inelastic demands pay higher prices). As part of that identification, they must be able to implement different prices for those customers. Finally, firms must be able to prevent resale. If consumers who can buy at low prices are able to turn around and sell to the consumers willing to pay a high price, then firms lose their ability to sell to the high price consumers. Price discrimination comes in three different categories. First-degree price discrimination, also called perfect price discrimination, is when firms are able to charge each consumer their maximum willingness to pay. Car sales that involve negotiation are an attempt at first-degree price discrimination. Data mining is a growing tool to help firms toward first-degree price discrimination. Second-degree price discrimination involves things like volume discounts or frequent customer cards. The idea is not to charge different prices to every customer but to allow customers to self-select into different price points for the producer to increase profit. Third degree price discrimination alters prices based on demographics or other group characteristics. This is the category of price discrimination with student or military discounts or movie theaters changing prices by time of day. Firms can use a variety of ways to identify customers based on their elasticity. Take airline tickets, for example. There are certain days of the week to travel when ticket prices are lower, and people can often get tickets at a lower price if they purchase their tickets a few weeks in advance. Why? Because airlines are attempting to separate the elastic buyers (vacation travelers) from the inelastic buyers (business travelers). Who likely plans a trip at least a few weeks in advance? Vacation travelers. Who is more likely to need a

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ticket on short notice? Business travelers. Who is unlikely to travel over a weekend? Business travelers. Who can afford to pay more for their ticket? Business travelers. Firms can also sell different versions of a product. Consumers with a high value for a product will likely need all of the bells and whistles of the product, but consumers with a low value for a product might only need the basic. That is why you might see a “pro” version of software or a “student” or “home” version. Sometimes, businesses can separate high use customers, such as printers and ink or razors and razor blades. The cost to buy the printer or the razor might be low, but to continue using the product requires ink or razor blades and those are sold at a higher markup. Firms can also use bundling to extract extra revenue. This strategy led to the value meals at McDonald’s or computers with preloaded software. Bundling increases the value of the base product, allowing producers to sell the product for a higher price. Customers might also be more inclined to pay a higher price for an all- inclusive deal than to pay small amounts to continually add features or products. A similar approach is taken with all-inclusive resorts and wrist bands at fairs. There is comfort in knowing that you can pay one price and be done with paying. Price discrimination sounds bad, largely because of the word discrimination, but it can be beneficial to society. When people hear about price discrimination, they often think of charging higher prices to certain consumers, but in many cases, it is about lowering prices (coupons, student discounts, matinees, etc.). Since some consumers can pay a lower price, that brings them into the market and allows them to benefit from the exchange. When looking at value to society, economists generally look at the total amount of exchange that occurs. How much the consumer benefits and how much the producer benefits are certainly interesting, but ultimately it is the amount of exchange that occurs. With price discrimination, the amount of exchange certainly increases, though it does come with more benefit going to producers and less going to consumers. Just because producers benefit at the expense of consumers does not mean consumers cannot benefit from price discrimination. Take Uber’s surge pricing, for example. Surge pricing is a type of price discrimination. People who are going to use an Uber on a busy night, such as Friday or Saturday night are going to pay more for an Uber. However, by charging more, Uber also attracts more Uber drivers to work on those busy nights. Without these additional drivers, Uber customers looking for an Uber on Friday or Saturday night would likely have long waits for an Uber or may not be able to get an Uber at all. Similarly, hotels charging higher prices during conferences, sporting events, and even natural disasters discourages demand and encourages consumers to be efficient in their consumption. By encouraging efficient consumption, there will be more rooms available for other people. Without the higher prices, more people would be left out. Certainly, this all works to the benefit of the producers, but it also works to the benefit of the consumer, and that is an important feature of price discrimination that should not be overlooked. It is another benefit of a free market system. Even if producers are acting in their own best interest, the benefits of those self-interested actions help other people.

Reference Porter, P. K., & Thomas, C. R. (2010). Public subsidies and the location and pricing of sports. Southern

Economic Journal, 76(3), 693–710. https://libraryresources.columbiasouthern.edu/login?url=http://search.ebscohost.com/login.aspx?direc t=true&db=bsu&AN=47776241&site=ehost-live&scope=site

ECO 6301, Economics for Managers 1

Course Learning Outcomes for Unit VI At the end of this unit, you should be able to:

4. Evaluate strategic pricing decisions. 4.2 Describe the different types of auctions and the benefits of each.

7. Explain the implications of uncertainty in managerial decision-making.

7.2 Illustrate how to use expected value calculations to deal with uncertainty. Required Unit Resources Chapter 17: Making Decisions with Uncertainty (ULO 7.2) Chapter 18: Auctions (ULO 4.2) Article: Auctions versus Negotiations: The Effects of Inefficient Renegotiation (ULO 4.2) This article reinforces the concepts of auctions and negotiations. Unit Lesson Lesson: Uncertainty and Auctions (ULOs 4.2, 7.2) This lesson introduces you to the topics covered in this unit.

Expected Value Examples in economics often assume a certain level of knowledge about the market, but this is often not the case. Firms often face uncertainty in their decisions. Firms can use expected value to deal with uncertainty. Expected value takes the probability of certain outcomes to arrive at a weighted average outcome. This concept is best illustrated with an example. Assume there are two possible outcomes for a game, such as flipping a coin. The outcome of heads is likely to occur 50% of the time. If heads occurs, you win $1. The outcome of tails is likely to occur 50% of the time. If tails occurs, you lose $1. What is the expected value of this game? We can determine this by simply multiplying the payout by the probability that payout will occur and then summing the products for each outcome. E[X] = ph * xh + pt * xt where X is the payout of the game, p is the probability, x is the payout for a particular outcome and the subscripts h and t stand for heads and tails, respectively. In the example described: E[X] = 0.5 * $1 + 0.5 * $1 = $1 The expected value of the game is $1. You can imagine this simple example could be considerably complex with different outcomes and multiple probabilities to match. Obviously, a very important part of calculating expected value is to get the probabilities right. Decision-makers should be aware that their probabilities are likely not correct. A good way to handle this is to run multiple scenarios with different probabilities. A growing opportunity for firms is to use data analysis to model probabilities. When using data, however, firms need to be conscious of selection bias. Selection bias occurs when there is some difference in the data used

UNIT VI STUDY GUIDE Uncertainty and Auctions

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UNIT x STUDY GUIDE Title

in the model probabilities that is not present in the target population. For a simple example of this, consider exit polls at elections. Pollsters survey voters coming out of voting booths to see how they voted and then make predictions on how the election will turn out based on those surveys. What happens, though, if pollsters primarily go to urban polling places to survey voters and do not go to rural polling places? If urban and rural voters vote the same way, this is not a problem, but if there are fundamental differences between how urban voters vote and how rural voters vote, then the surveys will be inaccurate. The surveys will likely be an accurate representation of how urban voters vote but not how voting is cast as a whole. Imagine a company making a similar mistake when marketing a new product. Uncertainty can never be completely eliminated, but firms can take steps to try to make informed decisions and minimize potential damage from unexpected events occurring.

Auctions You are probably most familiar with online auctions from websites like eBay. You might have gone to an antique auction when you were younger (possibly dragged there by a parent or grandparent). If you live near ranchers, you might have gone to a cattle auction. You have probably seen auctions portrayed on TV. You might have seen a silent auction at a charity. When sellers are unsure of the market value for their product, they can use auctions to make their sales. Auctions allow customers to bid for the product and thus reveal their value. Auctions help sellers sell their product and gain more information about the demand for their product. As seen from the previous paragraph, auctions can take a variety of forms. Auctions are often portrayed with somebody standing in front a room talking quickly and people in the audience bidding quickly. These are called oral auctions or English auctions. In these auctions, people make successive, increasing bids until only one bidder remains. The last remaining bidder gets the item at the last price they bid. So ultimately, the price is set marginally above the value of the second highest bidder (that is, a small amount above the value the second highest bidder holds). A few points about oral auctions are listed below.

1. First, the greater losing bids there are in an auction, the higher the winning bid amount will be. This point should make sense. The price will still go no higher than the highest valued bidder, but if the closer other bidders are to valuing the product similar to the highest valued bidder, the higher the winning bid will have to be.

2. Second, the more bidders there are in an auction, the more likely there will be other high valued bidders. On eBay, for example, ten-day auctions return 42% higher prices than three-day auctions as more time attracts more bidders (Froeb et al., 2018).

3. Third, there is an important piece of information that is never disclosed in an oral auction: What is the value the highest bidder holds for the product? All sellers know from an oral auction is that somebody valued the product more than the product sold for.

An auction that addresses this problem is a second-price auction, also called a Vickery auction. Second-price auctions are sealed-bid auctions, as opposed to the very public oral auction. There are also not multiple rounds of the auction where bidders can outbid the last bid. This is a type of sealed-bid auction where bidders submit a bid without knowing the other bids. The product is still awarded to the highest bidder, as in the oral auction, but rather than paying their bid, they pay the second-highest bid. A second-price auction encourages bidders to bid more aggressively and closer to their actual value (in fact the optimal strategy is to bid exactly their value) for the good since they know they will not have to pay their value, they will pay the bid of the second highest bidder. The outcome of the second-price auction is the same as the oral auction (the ultimate price is equal to, or just above, the value of the second-highest bid), but there are several benefits with a second-price auction that are not present with an oral auction.

ECO 6301, Economics for Managers 3

UNIT x STUDY GUIDE Title

1. First, as mentioned, bidders are encouraged to bid more aggressively. This aggressive bidding will likely result in a higher price bid by the bidder with the second highest value. To see this, imagine an oral auction where the second-highest value bidder infers from the highest-value bidder that they will not be able to outbid the highest value bidder. The second-highest bidder might stop bidding early knowing it is futile. Leaving the bidding early results in a lower ultimate price for the seller.

2. Second, second-price auctions can be conducted from anywhere and bidders do not have to be present. Second-price auctions were popular with stamp dealers as far back as the 19th century (Froeb et al., 2018). Saving bidders the cost of travel (both explicit and opportunity) increases the net value for the product to the bidders, which can also increase bids.

3. Third, and addressing the information shortcoming discussed with oral auctions, second-price auctions give the seller information on the maximum value for their product since people, including the winning bidder, will bid their maximum value.

Now, reading about a second-price auction might lead to the question, “Well, why not do everything with a second-price auction but make the highest bidder pay the price they bid?” The problem with this approach is that bidders are actually incentivized not to bid their maximum value. Since the winning bidder ultimately has to pay their bid, they don’t want to pay their maximum value. If they did, they would be left with no profit (that is, the difference between their value and what they pay) and bidders are technically indifferent between winning and losing the auction. That means that bidders have an incentive to shade their bid. The seller would not get accurate information on bidders’ value and would potentially get a lower price as all bidders shade their bids.

Collusion and Irrational Behavior Auctions can lead to attempts at collusion, called bid rigging. In bid rigging, a group of bidders work together to keep down bids so that somebody from the group wins the auction at a bid lower than it otherwise would have been. Bid rigging is more likely to occur in smaller, frequent auctions. The smaller size increases the likelihood of communication between bidders and the frequency gives more opportunity to refine the rigging and punish members of the group that attempt to cheat. Collusion is also more likely in oral auctions than sealed-bid auctions, giving another benefit to second-price auctions over oral auctions. Finally, bid rigging is more likely when the winner of an auction is identified. If bidders can win in secret, there is an incentive to cheat (recall game theory from Unit IV). Auctions can sometimes lead to irrational behavior. This irrational behavior is particularly true in oral auctions where the desire to win overtakes the actual desire for the product being bid on. Oral auctions, more than sealed-bid auctions, are likely to suffer from over bidding. For producers, though, this can mean a higher winning bid. Bidding more than the value for the product can lead to the winner’s curse, where the winner of an auction is actually worse off for having won the auction.

References Froeb, L. M., McCann, B. T., Shor, M., & Ward, M. R. (2018). Managerial economics: A problem solving

approach (5th ed.) [Vital Source Bookshelf version]. https://online.vitalsource.com/#/books/9781337468015

Herweg, F., & Schmidt, K. M. (2017). Auctions versus negotiations: The effects of inefficient renegotiation.

RAND Journal of Economics, 48(3), 647–672. https://libraryresources.columbiasouthern.edu/login?url=http://search.ebscohost.com/login.aspx?direc t=true&db=bsu&AN=124623600&site=ehost-live&scope=site

ECO 6301, Economics for Managers 4

UNIT x STUDY GUIDE Title

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

In order to check your understanding of concepts covered in this unit, complete the Unit VI Check For Understanding activity. Unit VI Activity Alternate Format PDF NOTE: Be sure to maximize your internet browser so that no part of the presentation gets cut off.