A student spends he “conspicuous consumption” bud , M, on ski lift passes (x) an

Question

A student spends he “conspicuous consumption” bud , M, on ski lift passes (x) and shoes (y). The price of a ski lift pass is Px an the price of a pair of shoes is p. Her utility from the consumption of the two goods is U(x, y) = 2y +y.

a) What is the student’s budget set? Her budget line?

b) Draw a hypothetical diagram representing the choices available to this student, her preferences over those choices, and her consumption choice.

c) What is the marginal rate of substitution of ski lift passes for shoes? What is its interpretation? The slope of which line in the above graph shows the marginal rate of substitution?

d) What is the equation of an indifference curve?

e) What are the two conditions which must be satisfied for utility maximization? Look at the preceding diagram!

f) Determine the student’s demand function for ski lift passes and her demand function for shoes.

g) If the student’s income were to increase, what would happen to the demand curve for ski lift passes? Determine the student’s inverse demand function for ski lift passes.

h) Now assume that M = $500,Px $50,Py = $150. Draw the budget constraint, the maximum attainable indifference curve, and show the optimal consumption bundle? How many ski passes and how many pairs of shoes will the student purchase?

i) Assume again that M = $500, Px = $50, Py = $150. The student receives a $300 gift card which can only be used for ski passes. Draw the new budget constraint and determine the new optimal consumption bundle, assuming that the student has to make a choice from scratch (i.e. he receives the cash and the gift card at the same time). What would the optimal bundle be if the gift card could be used for either good?

Explanation / Answer

x= ski lift pass

y= pair of shoes

a) px(X) + py(Y) = M : Budget line

px(X) + py(Y) <=M : Budget set

c) U = 2X + Y

MRS = change in Y/ Change in X = 1/2

This means that consumer is willing to sacrifice 2 of Y for one X.

d)Equation of indifference curve U= 2X +Y

e) For utility maximizing:

px(X) + py(Y) =M

MRS should be diminishing

f) U=2(M-py(Y)/px) +Y

Differentiate wrt Y

-2py/px +1 =0

2py =px

g) If student's income increases demand for ski lift will increase or remain the same.

h) 50X + 150Y =500

X=4, Y=2

i) 50X + 150Y = 800

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