Exercicio de Microeconomia

Consumer Choice
Exercise 1.
Function U allows us to know how that agent orders different combinations of goods x e y according to his preferences. For each of the following representations what is the shape of the indifference curves and what is the marginal rate of substitution
(MRS)? What does that tell you about the agent’s preferences?
a. U  x  2 y

x y
b. U  min  , 
3 4 
c. U  xy
d. U  x 2  y
Exercise 2.
Consider the following utility functions:
a. U ( x, y)  ( x  y) 2
b. U ( x, y)  0.2 log x  0.5 log y
c. U ( x, y)  x 2  y
d. U ( x, y)  x  y
Compute the marginal rate of substitution (MRS) of x for y for each of the utility functions above. For each case, analyze the evolution of the MRS along the indifference curve. What information does the slope of the indifference curve at a given point give you?

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Exercise 3.
Suppose that you have 40 monetary units (m.u.) to spend on two goods, whose unitary prices are p1  10 e p2  5 .
a) Specify the budget constraint and represent it graphically.
b) If you spend all the income on good 1, how much of the good can you purchase?
And what if you spend all the income on good 2?
c) If the price of both goods varies by 10% and the income also varies by 10%, how will the budget constraint change? How would your answer change if only the prices varied in the same proportion?
d) Suppose that the price of good 1 increases to 20 m.u.. What is the new budget constraint? Represent it graphically.
e) How much of good 1 can you buy if you spend all of your income in it?
f) Redo a) for a 60 m.u. income and prices p1  20 , p 2  5 .
g) Compute the intersection point between the two budget constraints.
h) Identify the area that corresponds to the bundles that you can afford after the increase in your income and in the price of good 1, but that you could not afford under the conditions of a). Identify the area that corresponds to the bundles that you could afford initially