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Consumer Optimal Consumption and Demand Curve for Clothing, Ejercicios de Microeconomía

Suzie's utility function for consuming food and clothing, her marginal utilities, and how to derive her demand curve for clothing. The document also includes a graph showing her demand curves for clothing when her income is $200 and $300.

Tipo: Ejercicios

2020/2021

Subido el 15/10/2021

nicole-chavez-13
nicole-chavez-13 🇵🇪

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5.5 Suzie purchases two goods, food and clothing. She has the utility function U(x, y)
= xy, where x denotes the amount of food consumed and y the amount of clothing. The
marginal utilities for this utility function are MUx = y and MUy = x.
a) Show that the equation for her demand curve for clothing is y = I/(2Py).
b) Is clothing a normal good? Draw her demand curve for clothing when the level of
income is I = 200. Label this demand curve D1. Draw the demand curve when I = 300 and
label this demand curve D2.
a) At the consumer’s optimum we must have
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5.5 Suzie purchases two goods, food and clothing. She has the utility function U ( x , y )

= xy , where x denotes the amount of food consumed and y the amount of clothing. The

marginal utilities for this utility function are MU x = y and MU y = x.

a) Show that the equation for her demand curve for clothing is y = I/ (2 P y

b) Is clothing a normal good? Draw her demand curve for clothing when the level of

income is I = 200. Label this demand curve D 1

. Draw the demand curve when I = 300 and

label this demand curve D 2

a) At the consumer’s optimum we must have

y

MU

x

P

x

y

P

x

P

x

x + P y

y

= I

MU

y

P

y

x

P

y

Py

P

x

y

P

+ P

y

y = I

x  

2 P

y

y = I

y

I

y

b) Yes, clothing is a normal good.

Holding

P

constant, if

I

increases

y

will also increase.

A) y

x

P

x

P

y

P

y

y = P x

( x +10)

P

x

x + P y

y = I

P

x

x + P x

( x +10) = I

2 P

x

x + 10 P x

= I

2 P

x

x = I - 10 P x

B) I = 100

x =

2 P

x =

I

2 P

x

x =

P

x

P

x

P

x

50 ≥ 5 P

x

P

x

x