As we shall see in Chapter 15, a firm may sometimes seek to differentiate its product from those of its competitors in order to increase profits. In this problem we examine the possibility that such differentiation may be “spurious"– that is, more apparent than real and that such a possibil- ity may reduce the buyers' utility. To do so, assume that a consumer sets out to buy a flat screen television (y). Two brands are available. Utility provided by brand 1 is given by U(x, y1) = x + 500 ln(1 + y,) (where x represents all other goods). This person believes brand 2 is a bit better and therefore provides utility of U(x, y2) = x + 600 ln(1 + y2). Because this person only intends to buy one television, his or her purchase decision will determine which utility function prevails. a. Suppose px = 1 and I = 1000, what is the maxi- mum price that this person will pay for each brand of television based on his or her beliefs about qual- ity? (Hint: When this person purchases a TV, either Yı = 1, y2 = 0 or y, = 0, y2 = 1). b. If this person does have to pay the prices calculated in part (a), which TV will he or she purchase? c. Suppose that the presumed superiority of brand 2 is spurious-perhaps the belief that it is better has been created by some clever advertising (why would firm 2 pay for such advertising?). How would you calculate the utility loss associated with the purchase of a brand 2 TV? d. What kinds of actions might this consumer take to avoid the utility loss experienced in part (c)? How much would he or she be willing to spend on such actions?
As we shall see in Chapter 15, a firm may sometimes seek to differentiate its product from those of its competitors in order to increase profits. In this problem we examine the possibility that such differentiation may be “spurious"– that is, more apparent than real and that such a possibil- ity may reduce the buyers' utility. To do so, assume that a consumer sets out to buy a flat screen television (y). Two brands are available. Utility provided by brand 1 is given by U(x, y1) = x + 500 ln(1 + y,) (where x represents all other goods). This person believes brand 2 is a bit better and therefore provides utility of U(x, y2) = x + 600 ln(1 + y2). Because this person only intends to buy one television, his or her purchase decision will determine which utility function prevails. a. Suppose px = 1 and I = 1000, what is the maxi- mum price that this person will pay for each brand of television based on his or her beliefs about qual- ity? (Hint: When this person purchases a TV, either Yı = 1, y2 = 0 or y, = 0, y2 = 1). b. If this person does have to pay the prices calculated in part (a), which TV will he or she purchase? c. Suppose that the presumed superiority of brand 2 is spurious-perhaps the belief that it is better has been created by some clever advertising (why would firm 2 pay for such advertising?). How would you calculate the utility loss associated with the purchase of a brand 2 TV? d. What kinds of actions might this consumer take to avoid the utility loss experienced in part (c)? How much would he or she be willing to spend on such actions?
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.14P
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Transcribed Image Text:As we shall see in Chapter 15, a firm may sometimes seek
to differentiate its product from those of its competitors in
order to increase profits. In this problem we examine the
possibility that such differentiation may be "spurious"-
that is, more apparent than real and that such a possibil-
ity may reduce the buyers' utility. To do so, assume that
a consumer sets out to buy a flat screen television (y). Two
brands are available. Utility provided by brand 1 is given
by U(x, yı) = x + 500 ln(1 + y¡) (where x represents all
other goods). This person believes brand 2 is a bit better and
therefore provides utility of U(x, y2) = x + 600 In(1 + y2).
Because this person only intends to buy one television, his or
her purchase decision will determine which utility function
prevails.
a. Suppose p, = 1 and I = 1000, what is the maxi-
mum price that this person will pay for each brand
of television based on his or her beliefs about qual-
ity? (Hint: When this person purchases a TV, either
Y1 = 1, y2 = 0 or y, = 0, y2 = 1).
b. If this person does have to pay the prices calculated in
part (a), which TV will he or she purchase?
c. Suppose that the presumed superiority of brand 2 is
spurious-perhaps the belief that it is better has been
created by some clever advertising (why would firm 2
pay for such advertising?). How would you calculate the
utility loss associated with the purchase of a brand 2 TV?
d. What kinds of actions might this consumer take to avoid
the utility loss experienced in part (c)? How much would
he or she be willing to spend on such actions?
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