Derive a demand curve from the following utility table forPizza A. assume income

Question

Derive a demand curve from the following utility table forPizza

A.   assume income is $10, the price of each slice ofpizza is $1, and the price of each glass of beer is $2. Then changethe price of pizza to $2 per slice.

B.   Now change income to $12 and derive a demand curvefor pizza.

Slices ofPizza                  Totalutility                   Glasses ofbeer               Total Utility
1                                           200                                 1                              500
2                                          380                                  2                              800
3                                          540                                  3                              900
4                                          600                                  4                              920
5                                          630                                  5                              930

Explanation / Answer

A demand curve is a "curve" (or, in this case, a straightline) that shows the relationship between the price of something(on the Y axis) and the quantity sold (on the X axis). Ittakes two points to determine a line, so you need to find two (Q,P)points. The problem tells you that the points to use are thepoints where pizza costs $1 and where pizza costs $2. Thismeans you just need to figure out how many slices of pizza yourconsumer is going to choose at each price. . . The consumer wants to combine slices of pizza and glassesof beer until she (a) spends all her money and (b) gets themost utility she can get while spending all her money. To get the utility, add up the utility from pizza and the utilityfrom beer. For example, suppose the consumer buys 3 glassesof beer (for $6) and 4 slices of pizza (for $4). Then shegets 900 utils + 600 utils = 1500 utils. . . The tricky part, then, is to find the combination of beer andpizza that maximizes utility. . . . I don't use tables like this in my class; I usually make mystudents solve these things algebraically. There are two waysI can see to proceed: . 1) Brute Force. Find all the combinations of pizza andbeer possible at the price and income, calculate thetotal utility at each one, and pick the best. Theproblem makes this a bit easier by making it impossible to havemore than 5 slices of pizza, greatly reducing the number ofcombinations to search. . . 2) Calculate the Marginal Utility from adding eachslice/glass. The MU of the first slice is 200, and of thesecond slice is 180 (that is, 380-200). The MU of thefirst glass is 500, and of the second glass is 300.  At apizza price of $1, a slice of pizza costs half what a glass of beercosts, so look at the combinations around the point where the MU ofbeer is twice the MU of pizza. . . Your teacher probably worked something like this in class, atleast as far as maximizing utility goes. . . Once you've found how many slices of pizza you predict you eatat P=$1, you have your first point on your demand curve. Nowchange the price of pizza to $2, and repeat the same exercise, toget the second point. Graph those two points and draw theline that goes through them, and you have a demand curve. . . In part (b), you get to repeat part (a), but this time demandhas been shifted by an increase in income.

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