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(solution) 1. Emily's income is $120. She spends her entire income on books.


1. Emily's income is $120. She spends her entire income on books. Emily considers paperback and electronic books to be perfect substitutes, and she is always indifferent between one paperback book and one electronic book. Initially, the price of a paperback book is $15 and the price of an electronic book is $10. Then the price of a paperback book falls to $8. Which of the following statements is true?

A. For paperback books, the income and substitution effects have opposite signs.

B. For paperback books, both income and substitution effect are zero.

C. For paperback books, the income effect is 3 and the substitution effect is 12.

D. For paperback books, the income effect is 4 and the substitution effect is 9.


2. Consider a consumer with preferences:

    u(x,y)=xy, (MUx=y, MUy=x),

facing prices Px=2 and Py=1 and having an income of M=24. Assume now that the price of good X increases to P'x=8.0. Calculate the substitution effect of the demand of good x associated with this price change. No unit, no rounding.


3. Consider a consumer with preferences
      U(x,y)= 2?x + y, (Mux=1/?x, MUy=1)
These preferences have a declining MRSxy. Assume that Px=1 and Py=1 and that the consumer has an income M=100. Calculate the income effect associated with good x if the price of good x increases to P?x=2. No units no rounding.


4. Consider a consumer in an economy with two goods, x and y. Prices are Px=3 and Py=1. Preferences of this consumer are such that for any possible income and given the prices above, the following is true at any bundle: MUx/Px> MUy/Py
Assume now that the income of this consumer increases by $90. Calculate the change in demand for good x associated with this change in income.

5. Assume an economy with two goods, x and y. A consumer's demand for good x is given by x=M/Px+Py.
Good x and good y are both normal goods. True or False?


6. Consider an economy with two goods x and y. Assume a consumer has preferences u(x,y)=xy.
The consumer's optimal bundle consists of positive amounts of good x and good y. Prices are Px=8 and Py=1. What is the marginal rate of substitution (MRSxy) of this consumer at his or her optimal bundle? No units, no rounding.


7. Consider Bert who has to decide between food with a price of 1 per unit and leisure time. To afford consumption. Bert has to work. Draw a diagram with leisure on the x-axis. Notice that leisure time is at most 15 hours (because Bert has to sleep). Suppose that Bert likes both leisure and consumption and that his MRS is declining. Suppose also that at the current wage rate, Bert chooses not to work at all.
Is the following statement true: A wage decline cannot induce him to increase his work hours. True or False?


8. Assume an economy with two goods, x and y. A consumer has preferences
U(x,y)=xy, (Mux=y, MUy=x).
Prices are Px=1 and Py=1. The consumer has an income of M=160. Calculate the CV ?Compensating Variation?if the price of good x increases to Px?=4. No units, no rounding.


9. Molly enjoys writing on paper. Currently, the price for 100 sheets of paper is $2. Molly?s demand for paper is given by Qp=525-5000*Pp
Where Qp stands for her demand for sheets and Pp stands for the price of a single sheet of paper. The government now imposes a tax of $0.5 on each pack of paper with 100 sheets. Therefore, the price of 100 sheets of paper rises to $2.5. Notice that Molly does not have to buy 100 sheets at a time. She can purchase individual sheets. Calculate Molly?s change in consumer surplus (final CS-initial CS). No units, round to 2 decimal places.


10. Calculate the tax revenue that the government collects from Molly in the previous question. Which of the following statements is true?
A. The magnitude of the tax revenue is twice as large as the magnitude of the loss in consumer surplus that Molly experiences.
B. The magnitude of the tax revenue collected is exactly equal to the magnitude of the loss in consumer surplus that Molly experiences.
C. The magnitude of the tax revenue collected is smaller than the magnitude of the loss in consumer surplus that Molly experiences.
D. The magnitude of the tax revenue collected is larger than the magnitude of the loss in consumer surplus that Molly experiences.

 


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