mikro-1 Susulan praktikum 2

CHAPTER 2
THE MATHEMATIC OF OPTIMIZATIONS

TRUE-FALSE

1. The first order condition state that any activity that contributes to the agent’s goal should be expanded up to the point at which the marginal contribution of further expansion is highest.

2. The Lagrangian multiplier can be intrepreted as the implicit value or shadow price of the objective function.

3. The envelope theorem is useful for examining how these optimal choices change when the problem’s parameters change.

4. b = f(x), when b is constant, then db/dx < 0

5. d / dq = 0 is a sufficient condition for an optimization process.

6. The elasticity ey,x will have different sign with the partial derivative y /

7. When the elasticity is calculated, there are unit-free -- the unit of measurement “cancel out” because they appear either in numerator or denominator.

8. Lagrangian multiplier method is used for solving unconstrained maximization problems.

9. When a function is homogeneous of degree 0 (zero), a doubling of all of its arguments, doubles the value of the function itself. But for function that are homogeneous of degree 1 (one), a doubling of all its arguments leaves the value of the function unchanged.

10. Young’s theorem show that, for homogeneous function, there is definite relationship between the values of the function and the values of its partial derivative.

ESSAY

1. Explain following theory briefly:

a. Envelope theorem

b. Young’s theorem

c. Implicit function

d. Euler’s theorem

2. What is the different between cardinal and ordinal properties?

3. Explain following statement with mathematical explanation and draw the proper graph!

“First order condition is a necessary condition for an optimal condition, but not a sufficient one.”

4. What is elasticity? How it’s measured? Can it be calculated through “logarithmic differentiation”? Give an example!

5. Suppose U (x,y) = 5 + 2

a. Calculate the partial derivative U /

b. Evaluate these partial deriative at x=2 , y = 3

c. Write the total differential for U

d. What is the implied trade off between x and y holding U constant?

6. Explain about the Lagrange multiplier. Why sometimes it’s used as shadow price?

7. Suppose a firm’s total revenue depend on the quantity of output produced (q) ccording to the function: R = 50 q -

With total cost: C = + 40q + 150

a. What level of output should the firm produce in order to maximize profits? What will profits be?

b. Show the second order condition for a maximum are satisfied at the output level found in part (a)

8. Suppose that f (x,y) = xy. Find the maximum value for f if x and y are constrained to sum to 1. Solve this problem in two ways : by substitution and by using the Lagrangian multiplier method.

9. Suppose y is a function of two variables dan .

y = - + 24

Use envelope shorcut to measure the optimal value of y (y*) changes when a parameter of it’s function changes.

10. Rachmat’s utility function:

U = + where his income is $1000. If the whole income assume to spend fully for consumption of X and Y, what is the maximum utility he can reach if price of X $5 and price of Y $2?

*Use Lagrangian multiplier method to solvethis problem. Differ clearly about both objective function and its constraint!

yang dikerjakan :
T/F = All
essay : 1, 5, 6

mikro-1 Susulan praktikum 1

CHAPTER 1 ECONOMIC MODELS

TRUE-FALSE

1. No model can describe reality exactly.
2. Economics is the study of how scarce resources are allocated among alternative uses.
3. Alfred Marshall shows how observed prices can be taken to represent an equilibrium balancing of the production costs incurred by firm and the willingness of demanders to pay for those costs.
4. Microeconomic has provided some background on how economists approach the study of the allocation of resources.
5. Equilibrium is condition when supply is equals to demand.
6. Models are judged by how well they can explain economic events in the real world.
7. Ceteris paribus is assuming that all variable is constant.
8. Use of the ceteris paribus assumption does pose some difficulties for the verification of economic models from real-world data.
9. The production possibility frontier shows the different combinations of two goods that can be produced from a certain amount of scarce resources.
10. Microeconomics theory describe about aggregate economy.

ESSAY
1. Mr.Tarno is an employee which use personal vehicle for working. Its requisition function to gasoline the need gets to be figured deep following equation:
Q d = 10 - 0.6P + 0.003I
Where Qd constitute total amount refuels that requested while price as big as p, with outgrows proprietary money as big as I. if assumed that proprietary money Mr Tarno is as big as $55.000, therefore:

a. Get do one price apply while no gasoline which be asked for?
b. If prevailing market price is as big as $15, therefore gets if total consumed gasoline Mr.Tarno's?
c. Accord price on option b, count the elasticity of demand!
d. Account too its income elasticity!

2. Why does the economics use mathematics model? What does its purpose ?

3. Explain the criteria / that requisite model an economy is said well!

4. Word excess and lack for economic model purpose especially that gets mathematical character in troubleshooting economic!

5. One firm that don't compete to do price differentiation to its product, where is price function that variably it is as follows:
P1 = 169 – 3Q 1 , P2 = 196- 2Q 2 , meanwhile faced production cost monopolist that is TC = Q1 2 + Q 1 Q 2 + Q2 2 + 61. Of that information, determine to outgrow its price p 1 and p 2 one that has to be on the market that maximum firm profit, determine to outgrow it outgrows unrealized corporate that!

6. determine equilibrium the market if is known:
Q d. = 9 – 3P
Q s = 5P – 3
Then figures its balance condition!

7. From demand and supply function that acknowledged on number 6, if government taxes Rp5 per unit, therefore determinative outgrows equilibrium after marks sense taxes, taxes acceptance for commanding, its outgrows taxes which took on by producer, and outgrows it taxes that taken on by consumer! And figures molded condition!

8. From number problem 6 also, if government gives to subsidy as big as Rp2 per unit, equilibrium's determinative after marks sense subsidy! And figures after balance condition mark sense to subsidize!

9. Bespoke logistic determinative and offer if known by startup price one goods is as big as Rp2000 per unit, with requested goods amount is as big as 20 units, then price experiences ascension as big as Rp2250 per unit, with requested goods amount as 14 about unit!

10. CV. Padasukamania is one training and consultation service firm that have cost function in its activity management as TC = Q2 + 40 – 4Q, where q constitute activity frequency that is carried on. If price that is on the market by CV. Padasukamania on customer per meet is as big as Rp14.000.000, therefore determines average cost's function, cost is marginal, full scale revenue, average revenue, and marginal revenue this firm!
If firm production function its Q = L 0,6 K 0,4 as maximum, account a lot of labour and a lot of capital which be needed, with totaled cost that was issued by that firm is as big as 96, where does price wage per labour is as big as Rp3 and capital price per unit is as big as Rp4, computing also outgrows it output who can be resulted by that input combine!

T/F : all , if false, give the reason
essay : 1,5,6,7,8,10