Econ 302: Practice
Questions 4
Question 1: Solve Question 5.2 in the workbook.
Question 2: Solve Question 5.3 in the workbook.
Question 3:
Assume that there are two goods and that
a consumers chooses x1=2 and x2=4 (as optimal
consumption choice). The
consumer's income is m. Let
p1=3 and p2=2.
- Given this information, can you determine the MRS? If your answer
is yes, what is
the MRS?
- Does you answer change if the optimal consumption choice
is
x1=0 and x2=6.
Question 4:
Assume the preferences of a consumer are given by
u(x1,x2)=x1+4x2.
-
For what price ratio(s) p1/p2 can one get an
interior optimum?
- For what price ratio(s) do you definitely get a boundary optimum?
Question 5:
Assume the utility function of a consumer is given by
u(x1,x2)=min{x1,x2}.
-
Consider the Budget set from question
3 of the second Problem Set in the review section.
Find the optimal consumption choice (you can do it graphically. To
find the budget set, click on the above link to get to the problem
set, and then click on the question to get to the solution).
-
Same as above except use the utility function
u(x1,x2)=min{50x1,x2} and
the budget set from question
4.
Question 6:
A utility function is given by
u(x1,x2) =
log(x1+x2)+x1.
The resulting
MRS=-(x1+x2+1). Assume prices are
p1=2, p2=1 (in the following you will get boundary optima (follow this link for some hints!)).
- Find the optimal choice for m=1.5.
- Find the optimal choice for m=2.
- Find the optimal choice for m=3.
- Does the demand for good 2 increase or decrease as a
consequence of the increase of income.
Question 7:
In a particular country
low income households are supported via a quantity subsidy s on
electricity. That is, households who qualify for the program pay a
price of p-s per unit of electricity (where p is the regular price).
An economist who advises the government argues that
this program should be reformed. Specifically, the economist argues
the government should provide free electricity to low income
households up the a certain amount.
Any amount in excess is charged at the
regular rate p. The economics argues that if the government spends
the same amount of money in this alternative program then the
following would be the case.
- The low income households will be better off.
- Less electricity will be used.
A reduction of the demand for electricity would be especially
desirable as the country often faces brownouts.
Demonstrate by means of a graph that the economist is right
(assuming that preferences over electricity (good 1) and all other
goods (good 2) are convex and monotonic).
Hint: This question combines several different issues
discussed in class. First graph the budget lines without any program and
with the existing program. Graph an optimal consumption choice. Then
determine the budget line for the alternative program.
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