National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 31
1. Consider the case of a competitive firm whose production function is given by = 50
0,52 . Fixed costs is 1500, = 25, and = 2,5.
What is the maximum of firms profit?
2. In shortrun firms production function is given by = 12 2 + , where 1 an
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 17
Task 1.
Consider consumers with preferences (1 , 2 ) = min(1 , 2 ) over the two good 1 and 2 .
a) Consider a standard utility maximization problem. Each consumer solves the
problem
max min(1 , 2 )
1 ,2
b)
c)
d)
e)
f)
g)
s.t. 1 1 + 2 2
Solve fo
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 2.
Ex. 1
For the following utility functions identify:
(i)
MRS
(ii)
Whether they are convex or not
(iii) What preferences are strictly monotonous
(iv)
Sketch a bunch of the indifference curves
(v)
Assume, without solving any consumer choice proble
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 33
1. Suppose government sets a minimum wage and fixes it above the market equilibrium
level. What will be the effect on (a) employment in a perfectly competitive industry in
which all firms are equally efficient; (b) the number of firms operating
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 5
Task 1
A loves collecting stamps (1 ) but he also watch movies and his preferences are given with
the utility function: (1 , 2 ) = 4 ln(1 ) + ln(2 ). Each stamp cost 1 = 1 and each movie
2 = 7. As individual income is = 70.
First suppose that th
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 16
Task 1.
The market demand function for some good is = 28 5 and the market supply
function is = 2 + 10. Suppose the government wants to raise the price of a good to
$3.00 and is debating between (a) a price floor, (b) a price support program, (c
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 6
Task 1
There are only 2 goods in economy. The change in price of a particular good causes the
change in consumption of this good
a) by only substitution effect
b) by only income effect
Give an example of such preferences and sketch the graphs fo
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 7
Task 1
Some person consumes only 1 , 2 and his preferences can be described as
a) (1 , 2 ) = (1 4)(2 6)
b) (1 , 2 ) = min(1 , 2 )
3
This person has a sum of money equal 64. Given the prices for both goods: 1 = 1, 2 = 2.
In the point of the optim
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 21
Task 1
A monopolist cost function is () = 10 + 2 , > 1. An inverse demand function on the
production of this firm is () = 120 2.
a) Calculate an equilibrium
b) Calculate consumer surplus and producer surplus
c) What is the deadweight loss from
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 8
Task 1
Imagine an individual with the utility function of the form (, ) = 100
= 8000, = 60, = 1. The price of decreases to 40.
a) Calculate the change in consumer surplus
b) How consumer surplus changed because of net price effect only?
c) How
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 27
Task 1
Ivanov is a owner of a cottage facing the lake on the Karelian Isthmus worth $500000: The
location attractive as it is, however has one drawback. Occasionally in the spring heavy
rains raise the water level in the lake, flooding the hous
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
The budget constraint
1) In households budget constraint 1 is rationed, i.e. the level of consumption of good 1 is
fixed to be no larger than some amount, 1 . Will the effect be the same as if 2 was
stamped? (The government has provided a subsidy on good
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 18
Task 1.
In a pure exchange economy with two goods, x and y, the two traders, A and B, have utility
functions: (, ) = + 4 and (, ) = + 2. Their endowments are = (4,8)
and = (2,12).
a) Solve for their contract curve and draw in the Edgeworth box
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Standard accounts
Income Statement in EUR million (IFRS)
2011
2010
Sales
Revenue
44,096.0
35,441.0
Cost of Sales (function)
Cost of sales
36,000.0 29,706.0
Gross profit
8,096.0
5,735.0
SG&A (function)
Distribution costs
3,599.0
3,038.0
SG&A (function)
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
1.Overview of modern approaches to business models generation.
1.1.Business model concepts.
Whenever a business is established, it either explicitly or implicitly
employs a particular business model. A business model describes the
design or architecture o
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Balance Sheet
Period Ending
2015
2014
Assets
Current Assets
Cash And Cash Equivalents
21120000
13844000
Short Term Investments
20481000
11,233,000
Net Receivables
35889000
31537000
Inventory
2349000
2111000
Other Current Assets
9539000
9806000
Total Curre
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 3
Task 1
Assume there are 6 individuals with different utility functions (ag) and each
of them has a sum of money > 0 and consumes only 2 goods 1 , 2 . Prices
are given as 1 , 2 > 0. For each individual calculate how much 1 and 2 he
will consume.
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 23
Task 1
Consider that there are 2 firms selling the goods for some market. Given their cost functions: 1 (1 ) =
12 + 71 2 (2 ) = 22 + 132 . The demand for their production is given as well: () = 100 .
a) Assume that the firms compete by Cournot.
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 11
Task 1
The technology is described with the production function (, ) = . MRTSK,L (MRT
substitution of K with L) increased by 15%. Before this changes / ration used to be 3
and the elasticity of substitution of K with L is 0,3. What is the ratio
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 32
1. Suppose a person has a utility function = ( + 9)0,5 0,25 , where is consumption and
is leisure. Less sleep time an individual has = 16,5 hours a day. So, = 16,5 , and =
. is hourly wage.
a) How many hours per day will a person choose to wor
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 10
Task 1
For the following production functions (iiii) answer the questions (ae)
i)
ii)
(, ) = 1/2 1/2
(, ) = min(, 2)
iii)
(, ) = 2 2
1
a) What returns to scale each function gives the producer?
b) Find the marginal products of K and L
c) Iden
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 14
Task 1.1
For each of the following production functions (iii)
(i)
(1 , 2 ) = ln(1 ) + 2
(ii)
(1 , 2 , 3 ) = (1 + 2 + 3 ) , 0 < 1
Calculate:
a) Returns to scale
b) Demand function for production factors
c) Profit function
d) Supply function
By
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 25
Task 1
The Kelly Corporation has an opportunity to invest $1.5 million in a project that will
generate profits of $0.5 million at the end of the first year, $0.55 million at the end of the
second year, $0.6 million at the end of the third year,
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 22
Task 1
The industry is dominated by two major competitors: A and B. Both companies have
similar technology allowing each firm to produce a good at a cost of $20. Accordingly, their
costs functions are given by: ( ) = 20 and ( ) = 20 .
In order
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 24
Task 1
Geralds income in the first year is 1 = $200 and in the second 2 = $200. Assume that the
interest rate is = 100%: (His time horizon is limited to these two years.)
(a) Find PV and FV of Gerald's income.
(b) Show on the graph Gerald's bud
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 9
Task 1
Over a threeyear period, an individual exhibits the following consumption behavior:
1
2
1 2
Year 1
3
3
7
4
Year 2
4
2
6
6
Year 3
5
1
7
3
Is this behavior consistent with the strong axiom of revealed preference?
Task 2
A person F chooses
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 34
1. (Monopsony discrimination) A monopsonist in the labor market faces a relatively
inelastic supply of female labor and hence pays its female employees a lower wage than its
male employees even though the two groups are equally productive. What
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 26
Task 1
Suppose that Lauras utility function is () = , where is wealth.
(a) Is she risk averse? Show mathematically.
(b) Suppose that Laura has an initial wealth of = $100.How much of a risk premium would she want to
participate in a gamble that
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
Seminar 12
Task 1
A farmer has a production function = () = . A unit of labor costs . Desired output
for the farmer is . Find his cost function.
Task 2
An output of some firm is described as follows: = (, ) = . Wages are fixed at the
rate =
(weekly) and
National Research University  Higher School of Economics
ECONOMICS 141

Fall 2015
The Maersk Group is a worldwide conglomerate that operates in some
130 countries with a workforce of over 89,000 employees. In addition to owning
Maersk Line, one of the worlds largest container shipping companies, Maersk is
involved in a wide range of ac