Chapter 12&18Uncertainty & Technology Flashcards
State of nature
The different outcomes of random events
Contingent consumption plan
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
Insurance
A say to transfer consumption from good states of nature to bad states of nature
State contingent budget constraint
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
The sell of insurance
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
Positive affine transformation
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
Cobb Douglas expected utility function
C1^π*C2^π can also be described as
π1ln(c1) +π2ln(c2)
Risk averse
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))
Risk loving
The consumer is said to be risk loving if she prefers a fair gamble to the expected value
Convex utility function
Risk neutral
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
Risk spreading
It’s consumer spreads his best over all of the other consumers there by reduces the amount of risk he bears
Diversification
Diversification allows for an investor to reduce the overall risk of investment while keeping the expected payoff the same
Production function
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)
Formal definition of production function
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)
Marginal productivity of labor MPL
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
Marginal productivity of capital
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
Eventually diminishing marginal productivity
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
Average productivity
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
Relationship between APL and MPL
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
Isoquants
Isoquants show the possible substitutions of one input for another that are capable of producing the same output
(Similar to indifference curves)
Marginal rate of technical substitution (MRTS)
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
Hypothesis of diminishing of MRTS
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⬇️
Return to scale
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)
Perfect substitute production function
(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
Perfect complements production function
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
Cobb-Douglas production function
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
Probability Distribution
A probability distribution consists of a list of different outcomes – in this case, consumption bundles – and the probability associated with each outcome.
