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
b. U min ,
c. U xy
d. U x 2 y
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?
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 but you cannot afford now. In which situation are you better off?
Suppose that you have a certain income level and that if you spend it all on goods x and y you can afford bundle x, y (3,8) or bundle x, y (8,3) . a) Plot these two bundles and the budget constraint.
b) What is the price of one unit of good x? (in terms of y)
c) If you spend all of your income on good x, how many units can you afford? d) Suppose that there is a rationing situation in which the consumption of goods x and y is limited to 9 and 11 units respectively. Draw the budget constraint under these conditions.
The income of a certain consumer is 120 m.u. being totally spent on goods x and y. The price of y is 3 m.u.. The price of x is not constant, depending on the quantity bought of that good as follows:
if 0 x 20 , then the price of x is 4 m.u.;
if 20 x 40 , then the price of x is 3 m.u.;
if x 40 , then the price of x is 2 m.u..
a) Represent graphically the budget constraint of this consumer b) Suppose now that the price of the first 20 units is always 4 m.u.; for each additional unit (after the 20th unit) the price becomes 3 m.u.; finally for each additional unit (after the the 40th) the price decreases further to 2 m.u. Represent 2
graphically the budget constraint for the case that the consumer’s income is 180 m.u.
Consider the problem of a farmer who allocates his income to consuming diesel (x) and food (y). Knowing that small farmers spend large amounts of money on diesel, the government decided to give them a subsidy of s per liter of diesel. This subsidy is only given when consumption is lower than x liters of diesel. a) Write the budget constraint before and after the government subsidy. Represent it graphically.
b) Suppose that the representative farmer consumes the bundle ( x0 , y 0 ) , with x0 x . Imagine that instead of subsidizing the price of diesel, the government gives an equivalent monetary compensation, such that...
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