Chapter 12&18Uncertainty & Technology

Question 1

State of nature

Answer 1

The different outcomes of random events

Question 2

Contingent consumption plan

Answer 2

A specification of what will be consumed in each differ t state of nature (each different outcome of a random process)

Contingent means depending on something not yet certain, so confident consumption plan means a plan that depends on the outcome of some event

In the cSe of the rainy and sunny days a contingent consumption would be the plan of what would be consumed given the various outcome of the weather

Question 3

Insurance

Answer 3

A say to transfer consumption from good states of nature to bad states of nature

Question 4

State contingent budget constraint

Answer 4

Cna: consumption do no accident
Ca: consumption is accident occurs

If you buy $K of accident insurance

• each $1 of insurance cost you γ
• Cna=m-γK
• Ca=m-L-γK+K or m-L+(1-γ)K

Question 5

The sell of insurance

Answer 5

The sell side of insurance market is divided into a retail component, which deals directly with the end buyers, and a wholesale component, in which insurers sell risk to other parties.

The wholesale part of the market is known as reinsurance market

Question 6

Positive affine transformation

Answer 6

We say that a function ν(υ)=αυ+β where α >0. A positive affine transformation simply means multiplying by a positive number and adding a constant

Economists say that an expected utility function is unique up to Ian affine transformation. This means that you can apply An affine transformation to it and get another expected utility function that represents the same preferences. But any other kind of transformation will destroy the expected utility property

Question 7

Cobb Douglas expected utility function

Answer 7

C1^π*C2^π can also be described as

π1ln(c1) +π2ln(c2)

Question 8

Risk averse

Answer 8

A consumer is that to be risk-averse if he prefers the expected value of his wealth rather than the fair gamble (expected utility from gamble)

Cobb Douglas utility functions are risk-averse

Risk averse have concave utility functions

π1(ln(c1))+π2(ln(c2))

Question 9

Risk loving

Answer 9

The consumer is said to be risk loving if she prefers a fair gamble to the expected value

Convex utility function

Question 10

Risk neutral

Answer 10

The consumer is said to be risk neutral if she is in different between a fair gamble and expected value of wealth t

This is a case of linear utility

Question 11

Risk spreading

Answer 11

It’s consumer spreads his best over all of the other consumers there by reduces the amount of risk he bears

Question 12

Diversification

Answer 12

Diversification allows for an investor to reduce the overall risk of investment while keeping the expected payoff the same

Question 13

Production function

Answer 13

The principal activity of any firm is to turn inputs into outputs

We model the relationship between inputs and outputs as a production function

Q=F(L,K,M,E…)
Simplified Q=F(L,K)

-Q=flow of outputs (physical units per unit of time)
-L=flow of labor inputs( person hours per unit of time)
-K=flow of capital inputs (machine hours per unit of time)
-M=flow of material inputs (per unit of time)
-E=flow of energy inputs( per unit of time)
…. And so on

P= price of outputs ($per physical unit)
W=wage rate ($per person hour) assumed constant unless told otherwise
R=rental rare ($ per machine hour)

Question 14

Formal definition of production function

Answer 14

The firms production function for a particular good Q

Q = F (L, K)

Shows the maximum amount of a good that can be produced using alternative combinations of labor (L) and capital (K)

Question 15

Marginal productivity of labor MPL

Answer 15

MPL (L,K)= ρF(L,K)/ρL

The partial derivative of the productivity function with respect to labor L

Given the current use of L units of labor and K units of capital how much extra production could be achieved with one more unit of labor

Question 16

Marginal productivity of capital

Answer 16

MPK (L,K) = ρF(L,K)/ρK

The partial derivative of the production function with respect to capital K

Given current use of L units of labor and K units of capital, how much actual production could be achieved with one more unit of capital

Informal definition; if we increase the unit of capital by one how much actual production is achieved

Question 17

Eventually diminishing marginal productivity

Answer 17

As you at progressively more of a given input, holding the other input constant, the game to help but become smaller, or the marginal increase is smaller.

You only need a certain amount of people to Max productivity. If you add another labor then they start bumping into each other and productivity decreases

Question 18

Average productivity

Answer 18

When people say that an industry or firm has experienced a labor productivity increased they are usually referring to the average output per unit of labor

APL (L, K)= F (L, K)/ L = Q/L

Average capital productivity is similar APK (L, K) = F (L, K)/K = Q/K

Question 19

Relationship between APL and MPL

Answer 19

APL increases when MPL is above the curve and decreases when MPL is below it

Notice that the maximum APL is when APL equals MPL

Question 20

Isoquants

Answer 20

Isoquants show the possible substitutions of one input for another that are capable of producing the same output

(Similar to indifference curves)

Question 21

Marginal rate of technical substitution (MRTS)

Answer 21

The MRTS is equal to the ratio of the marginal productivity of labor and capital MRTS equals partial derivative of L/partial derivative K

MRTS=MPL/MPK

Tells us how small changes in L and k affect output along any specific isoquant.

ρQ=0 because output is constant

MRTS is the slope of the isoquant at point (L, K)

If we took away one unit of labor, how much extra capital would a firm need to maintain the same level of production as before

Question 22

Hypothesis of diminishing of MRTS

Answer 22

If you have Morel, then when you get up a unit of Al, then it takes less K to bring you back to the same production level.

Test: does L increasing and K decreasing imply that MRTS is decreasing

L⬆️, K⬇️= MRTS⬇️

Question 23

Return to scale

Answer 23

How does output respond to increases in all outputs?

Constant returns to scale: F(mL,mK)=mF(L,K)
Increasing returns to scale: F(mL,mK)>mF(L,K)
Decreasing returns to scale: F(mL,mK)

Question 24

Perfect substitute production function

Answer 24

(L, K,) = aL+bK
Marginal productivity we:
MPL: a
MPK=b

Average productivities
APL= a+bK/L
APK=aL/K+b

MRTS: -MPL/MPK =-a/b

Constant returns to scale

Question 25

Perfect complements production function

Answer 25

F(L,K)=min[bL,aK]

bL=aK
K=b/aL
Slope: b/a

Marginal productivities:
MPL: undefined
MPK:undefined

Average productivities
APL: Q/L
APK:Q/K

Constant returns to scale

MRTS:Undefined

Question 26

Cobb-Douglas production function

Answer 26

F(L,K)=AL^αK^β

Marginal productivities:
MPL=αAL^(α-1)K^β
MPK=βAL^αK^(β-1)

Average productivities:
APL=

MRTS=-MPL/MPK=-aK/bL

Question 27

Probability Distribution

Answer 27

A probability distribution consists of a list of different outcomes – in this case, consumption bundles – and the probability associated with each outcome.