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Practice Problems

Problem : Nathan and Joe are shopping for video games. Nathan's demand function for video games is Q = 30 - 3P, and Joe's demand function is Q = 48 - 4P. What will their combined demand be if the price is $5? $11?

If we add Nathan and Joe's demand functions, we get:
At $5 a game, both Nathan and Joe will have positive demand for video games, and so we can use the combined equation to get

Q = [78 - 7(5)] = 43 games.

At $11 a game, however, Nathan's demand function gives negative demand, which we know means he just has 0 demand for video games. In this case, we ignore Nathan's function, and just use Joe's to figure out their combined demand, since using the combined function would give the wrong answer.

Q = [48 - 4(11)] = 4 games.

Problem : Michelle is shopping for shirts. She chooses one, then notices that the shirts are on sale, and gets another two shirts. How can you explain this with a graph?

This is an example of moving along a demand curve. Nothing except for the price has changed, so when Michelle notices the price change, she buys more shirts.

Changes in Price and Changes in Demand

Problem : Jenn's parents increase her allowance, so she spends more money on candy every week. How can you explain this with a graph?

This is an example of a shift in Jenn's demand curve. She has a permanent increase in her income, so she begins to buy more, even though the prices haven't dropped.

A Shift in Jenn's Demand Curve

Problem : Kris and Tim's demand curves for playing cards look like this:

Tim and Kris's Demand curves for Playing Cards
Who wants more when the price is $3 a pack? $4 a pack? What is their combined demand at $4 a pack?

As we can see on the graph, Kris will buy more than Tim if the price is $3 a pack, but if the price is $4 a pack, they will have equal demand for playing cards. At $4 a pack, they will each buy 3 packs, for a combined demand of 6 packs.

Tim and Kris's Demand Curves for Playing Cards

Problem : Emily decides to set aside $200 from her paycheck every month. How will this affect her demand curve? (You don't have to use specific numbers, just explain)

When Emily sets aside money from her paycheck, this is the same thing as a decrease in her income. Remember that when income increases, the demand curve shifts outwards to reflect the increase in spending. In this case, Emily's demand curve will shift inwards as she tries to economize more than usual. She will buy fewer goods, even if the prices don't change.

A Shift in Emily's Demand Curve