Is the certain amount of consumption that provides the same amount of utility as a risky choice.
Amount of money an individual would be willing to give up completely eliminate risk. Max willingness to pay to avoid risk and minimum willingness to accept to take on risk
RP = EV(c) - CE
Invested in different assets when outcome are perfectly positively correlated. More generally diversification will usally reduce risk and reduce the expected return. Stock mkt allows owners to diversify by not putting all wealth into one company. There is still aggregate risk (syestematic risk) to entire risk in stock market
how does firm choice lead to individual and market supply. How does interaction of consumer and firm choice determine what happens in the market.
- Firms have some tech that allows them to turn inputs into outputs
- We will use production function to represent the realtionship between inputs (L,K) and outputs q
q = f(L,K)
- assume production function is exogenous
the additional output a firm produces as a result of hiring one more worker. MPL = 2f(l,K)/2l
MPL is the slope of this graph that is often at low levels of production, the MPL increases because of gains from specialization made possible by the stock of capital.
q = f(L,K) = aL + bK
MPL = a and MPK = b
The marginal product of each good is constant. Low of diminishing returns does not apply
q = f(L,K) = min(aL,bK)
- ideal ratio of labor to capital
- accurately models production technology that faces bottlenecks
ex- shipping industry needs one truck for every truck driver or a computing industry needs a fixed ratio of ram processing power and storage to process computer programs
-this indicates that, for example, as a firm uses more and more labor it becomes more difficult to substitute labor for capital
Profit
Total revenue - total cost
P = Price of output x quantity of output - C(q)
Prices of inputs
production technology
All else equal, for a particular level of output, a firm minimizes its profit by minimizing its cost, we can derive the cost function by minimizing total costs for a particular quantity
In a competitive environment in a small industry, firms are price takers
wage rate and rental rate are exogenous
C = w x L + K x r
identifies all combinations of capital and labor the firm can hire for the same amounts. Slope = -w/r
Similar to budget line, except firm can choose its total cost
take a production function and find the cost function that tells us the cheapest way to produce q units of output. Firms want to produce f(L,K) while minmizing c = wL+rK
Similar to utility maximization problem where consumers wanted to maximized, but not overspend
Accomplish this by choosing L and K such that they produce units at the lowest possible cost
L and K are demanded for firm's inputs are endogenous to the cost minimization problem
Firms want to produce the level of output represented by the isoquant
When isocost and isoquant are equal --> MPL/MPK = w/r = MPL/w = MPK/r
C(q) = wL(q) + rK(q)
Tells us how a firm's total cost changes as their production changes. As q increases, cost should increase
C(q) is total cost function and MC(q) = C'(q) is marginal cost function and represents the slope of C(q) --> exponential
The firm is experiencing the law of diminishing returns because MC is increasing so each unit produced is getting more expensive. The marginal cost graph is convex
costs that vary with the quantity of output produced. Ex- wages, utilities, raw ingredients. The distinction between fixed and variable costs only matter in the short run
C'q = MC(q)>0
C'' = MC'(q)>0
Costs are positive and increase as we increase output. Marginal costs will increase at a constant rate so MC is linear. Quadratic functions are used simply for representing the law of diminishing marginal returns
Total Cost graph- exponential
MC cost graph- linear graph
Produce MC functions that are quadratic. Allow us to model a firm that benefits from specialization of low levels of production before eventually experiencing diminishing returns
Total cost graph- decreasing MC and then increasing MC
MC graph- increasing MPL (downward sloping), decreasing MPL (upward sloping)
Firms sell an identical product
All buyers/sellers are price-taker (no individual has control of the price)
Firms can start up in these industries and exist in this industry without substantial cost barriers. True in the long run, but not in the short run. In long run, firms will earn zero economic profit.
We can take the derivative of profit with respect to quantity to see how a change in production, causes a change in profit.
dprofit/dquantity = P -MC(q)
It starts high because of fixed costs, but decreases because of low marginal costs, before eventually being brought up by the law of diminishing marginal returns.
To avoid losses, firms would exit this market in the long run.
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