Answer to Question #259065 in Microeconomics for shemore

Question

 A consumer’s weekly income is $5000, the price of a cell phone is $1250, and the price of a watch is $500. What quantity of cell phones and watches will maximize the consumer’s utility if they spend their entire weekly income on cell phones and watches? Explain your answer using marginal analysis.                  

      I.          Suppose that this consumer’s income elasticity for watches is 5.4. what does this indicate about watches? If the cross-elasticity calculates to 0.8 what does this indicate about the relationship between watches and cell phones?

Answer 1

Solution:

Budget Constraint: I = PxX + PyY

Where: I = Income = 5,000

            Px = Price of a cell phone = 1,250

            Py = Price of a watch = 500

            X = Cell phone

            Y = Watch

5000 = 1250X + 500Y

MRS =$\frac{Px}{Py}$

$\frac{Y}{X} = \frac{1250}{500} = 2.5$

Y = 2.5x

Substitute in the budget constraint:

5000 = 1250x + 500y

5000 = 1250x + 500(2.5x)

5000 = 1250x + 1250x

5000 = 2500x

X = 2

Y = 2.5x = 2.5(2) = 5

U(x,y) = 2, 5

The quantity of cell phones and watches will maximize the consumer’s utility if they spend their entire weekly income on cell phones and watches = 2 and 5

= 2 cell phones

= 5 watches

1.). When the income elasticity of demand is 5.4, this indicates that watches are normal luxury goods since the income elasticity of demand is greater than one. That is, when income rises, individuals spend a higher percentage of their income on watches.

 

When cross-elasticity of demand is 0.8, this means that watches and cell phones are substitute goods, since the cross-elasticity of demand is greater than one. That is, when the price of watches rises, individuals will tend to substitute watches for cell phones and vice versa.