Micro Test 2
isoprofit line...what is the profit-maximizaiton problem graphically? what is the slope of the isoprofit line? what is the slope of the production function? what is the tangency condition
-all combinations of input goods and the output good that give a constant level of profit -find the point on the production function that has the highest associated isoprofit line -slope of isoprofit= w/p -slope of production function=marginal product MP1=w1/p
graphically demand curve facing firm for competitive firms
-horizontal at market price -nothing above market price -takes on entire market demand below price
what is happening when average variable costs are decreasing? what does this imply about the intersection?
-if the average variable costs are decreasing, it must be that the marginal costs (cost of producing one more unit of output) are less than the average variable costs in this range -if the average is decreasing, it must be that the cost of each additional unit produced is less than average up to that point so graphically when the AVC is decreasing, the MC is below it
what do we typically assume about production? (rate/scale)What can you conclude with this? (what term applies)
-increases at a decreasing rate -this is known as diminishing marginal product
average cost function...what assumptions lead to write cost function as c(y)
-the average cost function is simply y the cost per unit to produce y units of output cost function divided by y -the average cost function may decrease, remain constant, or increase over different levels of output -the factor prices are fixed at a predetermined level and only think of costs as depending on the output choice of the firm
what does the marginal cost curve measure? how does the marginal cost curve relate to average variable cost? (think limits)
-the change in costs for a given change in output -the variable costs are zero when output is zero so the marginal cost approaches the average variable cost as output approaches zero
demand curve facing the firm? (relationship between) what if you're the only firm in the market? so what does the demand curve summarize (constraints)
-the relationship between the price a firm sets and the amount that it sells -it is just the market demand curve because this measures how much of the good people want to buy at each price -thus the demand curve summarizes the market constraints facing a firm that has a market all to itself
Drawing the Marginal Cost Curve
1 Marginal cost starts out at the same level as average variable cost I Note if AVC is initially decreasing, MC will initially decrease as well 2 Marginal cost intersects AVC curve at AVC minimum 3 Marginal cost intersects AC curve at AC minimum
Deriving the average cost function. Explain AFC(y) what happens when you increase y to y=2? what would happen initially if you organized production in a more efficient way to AVC(y)
AFC(y)- as y increases the average fixed cost decreases towards zero AVC- when you increase y by 2, at worst variable costs will double so that average variable cost would remain constant -the average variable cost might even decrease initally
What will happen if a firm is making positive profits? (think other firms) Then what will happen to supply curve Then what will happen to market price Then what will happen to output
Because the firm is making positive profits, other firms will enter, shifting the supply curve out. This leads to a lower market price, so the firm will produce fewer units.
What profits are sustainable in the long-run? why? (think entering and exiting)
Can't have negative profits in LR; otherwise firms would exit the market Can't have positive profits in LR; otherwise firms would enter the market Thus firm profits must be zero in the long run
How do taxes affect producers and consumers in the long run? Why is this?(think where producers will supply at
Falls entirely on consumer. Producers will supply only at p ∗ = min AC, so tax cannot affect producer price at all
What is the marginal product of capital? f(L,K)=(L^1/4+K^1/4)^3
Find the marginal product of capital by taking the derivative with respect to K df/dk=3(L^1/4+K^1/4)^2 x 1/4K-1/4
what are only two possibilities when it comes to a firms optimal profit?
Firm is making zero profit Firm is making positive profits but has decreasing returns
What is the demand curve faced by the firm for perfect competition, assuming market price p (what if it sells above p or below)
If the firm prices above p* they sell nothing If the firm prices at or below the market price, faces the market demand curve
what does marginal cost measure
Measures how the cost of producing an additional unit of output changes as the total output level changes
Can a firm be profit maximizing if MP1>MC?
No, because if you added another worker, you would make more profit so you could not have been profit maximizing
Can firm be profit-maximizing if MP <MC?
No, because if you fired someone you would make more profit
What is the profit-maximizing quantity?Y=F(L,M)=50√L+100√M
Once you solve for profit-maximizing combinations of L and K through their first order conditions Plug these factor demands into Y to find profit maximizing quantity
what are the firm's total profit at this point? Profit=py-wL-K
Plug profit maximizing quantity into the equation and solve for profit
Calculate the profit-maximizing combination of labor and materials?
Profit=py-w1x1-w2x2 Max pf(x1,x2)-w1x1-w2x2 L,K Take first order condition with respect to K and L Solve for both L and K
how do you solve for long run total cost curve? (simple; short run is trickier)
Regular cost minimization. Set up Langrangian
What is the formula for the technical rate of substitution? f(L,K) What is it saying (*changes in input and output)
TRS= - (df/dL)/(df/dk) how much do we have to change the amount of input 2 to get the same level of output
what do you do when one of the variable is fixed (K)in the short run? (think what were cost function be in terms of and how you get to this point) Find short run cost curve
Take original production function and solve for the unfixed variable (L) Plug this into the cost function so you will now have a cost function in terms of both (Y) and fixed variable (K)
Profit Maximization (solving for factor demand curves)...How can you restate the FOC for the profit maximization problem? (2 ways Why does this hold?
The FOC is the Marginal Product=Marginal Cost -marginal product must equal marginal cost for a firm to be profit maximizing or MR=w MR=pMP
where is the only place a monopolist will produce ? (think in terms of demand curve)
Thus a monopolist will only operate in part of demand curve where demand is elastic (if anywhere)
What does the AC curve look like?where does MC curve intersect the AV curve?
U-shaped. MC curve intersects the AVC curve where the AVC curve is minimized
what does the first order condition of a competitive firm tell us (firm is choosing output where...)
a competitive firm will choose a level of output y where the marginal cost it faces at y is equal to the market price
when there are other firms in the market, what does a firm have to do? (think in terms of price and output)
a firm has to guess how the other firms in the market will behave when it chooses its price and output
Technology is the study of (actions and restrictions)...what kind of process is is it based on ? (one word)
a firms behaviors and the constraints imposed by customers, competitors and by nature -production process
a market is purely competitive if.. (think market price and output) a firm only has to worry about... so what are firms in a purely competitve market? (2 situations)
a market is purely each firm assumes that the market price is independent of its own level of output -a firm only has to worry about how much output it wants to produce; whatever it produces can be sold at one price; the going market price price takers- 1. many small firms and identical product 2. few firms, lowest price being offered is market price so all firms will sell at market price
how does a firm choose the amount to produce? What is the assumption about prices for firms? What kind of market is this? (how are firms taking prices)
a production plan so as to maximize its profits -a firm faces fixed prices for its inputs and outputs -when producers take the prices as outside their control as a competitive market
how do we describe a production relation with two inputs? (what curve)
an isoquant- set of all possible combinations of input 1 and 2 that are sufficient to produce a given amount of output
Path of the AVC (consider where it is decreasing)
as output increases, must be adding a number smaller than the average to the total so MC(y) < AVC(y)
MC(y)=AVC(y)
at the point that the average variable cost is niether increase not decreasing (the minimum)
why would you expect average variable costs to eventually rise? (what will fixed factors eventually do to the production process) Take for example that a building is a fixed cost. How does this sum up the average cost curve?
because if fixed factors are present, they will eventually constrain the production process -as production increases, average variable costs may remain constant for awhile, but as the capacity of the building is reached, these costs will rise sharply -the initial decline in average cost is due to the decline in average fixed costs; the eventual increase in average cost is due to the average variable costs which yields a u-shape
why will AVC eventually rise? why will average cost initially fall then rise
because there are fixed factors that constrain production due to declining fixed costs and then increasing variable costs
profit maximization problem facing a competitive firm. what do they ignore? where will the firm operate at? what if this condition didn't hold?
by definition, a competitive firm ignores its influence on the market price maxpy-c(y) y when marginal revenue equals marginal cost-where the extra revenue gained by one more unit of output just equals the extra cost of producing another unit if this condition didn't hold, the firm could always increase profits by changing its level of output
how is the supply curve of a competitive firm determined? (by what condition)
by the condition that the price equals the marginal cost
What does cost minimzation problem say in words? How do you solve? What is the constraint? Solve for optimal amount of labor and capital
choose inputs to find cheapest way to make output equal y min x1,x2 w1x1 +w2x2 s.t. f(x1,x2)=y L= w1x1=w2x2+ lambda(y-production function) FOC(L) FOC(K) FOC(Lambda)
when solving first order conditions in cost minimization problem, what are K* and L* referred to ? why?
conditional factor deamnd because they are conditional on the output level y
define: demand curve faced by the firm (what is the relationship between)
demande curve faced by the firm is the relationship between the price the firm sets (market price in case of perfect comeptition) and the amount it sells at that price
diminishing marginal product vs diminishing TRS (think about the difference when it comes to factors)
diminishing marginal product says how much extra output you get from each additional input holding other input FIXED diminishes diminishing TRS is about how the ratio of the marginal products-changes as we increase the amount of one factor and reduce the amount of the other factor
calculate the average variable cost c(y)=y^2+10
divide the variable cost by y AVC= y^2/y= y
1. what do you assume for cost curves to get the cost function equal to c(y)?
factor prices are fixed
what is our assumption about firms
firms are small (and hence cannot supply the whole market), they will price at the market price (if they sell at all)
How do you break down profit maximizing into two?
first look at how to minimize the costs of producing any given level of output and then we will look how to choose the most profitable level of output
minverse supply function...what does it say about firms who produce a lot vs a little in terms of marginal cost if they are both profit maximizing? how to solve for inverse supply function
gives price as a function of output a firm that produces a lot of output and a firm that produces only a little output must have the same marginal cost, if they are both maximizing profits p=MC(y)
what are the two important decisions a firm faces? (price and output) what would a firm do if there were no constraints? (both) What two constraints does a firm face?
how much it should produce and what price is should set if there were no constraints on a profit-maximizng firm, it would set an arbitrarily high price ad produce high output technological constraints- production function (only certain feasible combinations of inputs and output) which lead to economic constraints summarized by the cost function market constraint- a firm can only sell as much as people are willing to buy
what is the demand curve faced by firm in competitive market if they set a price below the market price
if firm prices below the market price they face the market demand curve
when does the shutdown condition occur? (b/c a firm would be better off doing what) why is this the case (think revenues and costs) what is the firm's supply curve?
if the average variable costs are greater than the market price, the firm would be better off producing zero units of output -because the revenues from selling the output don't even cover the variable costs -if it produces nothing it will lose its fixed costs, but it would lose even more if it continued to produce since a firm will only produce if its average variable cost is less than the price, the supply curve is the marginal cost curve that is above the AVC
increasing returns to scale
if we double each input; we get more than double output f(2x1,2x2) more than 2f(x1,x2)
long run vs short-run
in the SR-there is at least one factor of production (input) that is fixed in the LR-all factors of production can be varied
short run vs long run (inputs)
in the short run some inputs may be fixed at a certain level but in the long run, all factors can be adjusted
Cobb-Douglas returns to scale
increasing if a + b > 1 decreasing if a + b < 1 constant if a + b = 1
As firms enter one-by-one., what happens to the industry supply curve (2 things)? When will they stop entering? what happens ot the LR supply curve if the number of firms entering is very large?
industry supply curve moves out and becomes steeper Firms will enter until adding one more firm will lower equilibrium price below p then the LR supply curve is flat (ie perfectly elastic) at price p*
how does the optimal choice of factor 1 change as we increase its factor price w1? (think isoprofit curve and tangency condition)...what does this say about the relationship between factor demand curve and price?
isoprofit has slope w1/p -increase in w1 makes slope steeper, the tagency condition is now further left, so the optimal condition decreases -as price increases the demand for factor 1 must decrease
what does a competitive firm think if charges a price higher than the market price, at market, below?
it will sell nothing if it charges greater than market price -if it sells at the market price- it can sell whatever amount it wants -if it sells below the market price, it will get the entire market demand
when maximizing profits, the VALUE of marginal product of a factor should equal...why? (think what what happen if it pMP > w and pMP<w)
its price- pMP=w -the the value of marginal product exceeds its cost, then profits can be increased by increasing input 1 -if the profits are as large as possible then profits should not increase when we increase or decrease input 1
demand curve facing a firm (what does it depend on) vs market demand curve (what does it depend on)
market demand curve measures the relationship between market price and the total amount of output sold demand curve facing a firm measures the relationship between the market pricr and the output of that particular firm -market demand curve depends on consumer behavior while the demand curve facing a firm depends on consumer behavior but also the behavior of other firms
Through what equation does a monopolist maximize profits. What does revenue equal? Taking first order condition. Why is this different?
max p(y)y − c(y) y revenue is r(y) = p(y)y FOC MR=MC but the equation for marginal revenue is different because when the monopolist changes their output, price changes as well
short-run profit maximization formula (fix factor 2) let p be the price of output and w be the price of input
max pf(x1,x2fixed)-w1x1-w2x2 x1
Solving for factor demand curves Y=F(L,M)=50√L+100√M
maxpf(L,K)-wL-sK L,K take derivative with respect to L--FOC(L) take derivative with respect to K--FOC(K)
what does a factor demand curve measure?
measures the relationship between the price of a factor and the profit-maximizing choice of that factor
technical rate of substitution
measures the tradeoff between two inputs in production -how you have to substitute inputs to remain at the same level of output -slope of the isoquant
what does the cost minimization problem look like? What is the solution in words? What does the cost function measure? what are you looking for in terms of an isocost line?
min w1x1 +w2x2 s.t. f(x1,x2)=y x1x2 the minimum costs necessary to achieve the desired level of output the minimal costs of producing y units of output when factor prices are (w1,w2) -find the point on the isoquant that has the lowest possible isocost line associated with it
define cost function
minimum cost of achieving a given level of output
market demand curve and monopolies
monopoly faces the market demand curve
two assumptions of technologies (same as consumer assumptions)
monotonic-if you increase the amount of at least one the inputs, it should be possible to produce at least as much output as before convex-if you have two ways to produce an output, then their weighted average will produce at least that
quasi-fixed factor with example (when is it fixed when isnt it)
must be used in a fixed amount, independent of the output, but only as long as the output is positive -electricity for lighting -if the firm produces zero output, it doesn't have to provide lighting -if the firm produces positive output, it has to purchase a fixed amount of electricity for lighting
what happens when you change the price of the fixed factor? think isoprofit curve
no effect on the slope of the isoprofit line -optimal choice of factor 1 will not change, nor will the supply of output -profits will decrease
what does technological constraints on a firm mean? (think feasible) what is a firm trying to do (do what given what)
only certain combinations of inputs are feasible ways to produce a given amount of output -maximum possible output given amount of input
what would profit be if a firm decided to shut down? when should they shut down? (define shutdown condition)
only pay a fixed cost so profit would be -F -shutdown condition: firm should shut down if price is less than average variable cost at optimal quantity
fixed proportions example
producing holes inputs: men and hovels total number of holes that you can produce will be the minimum number of men and shovels you have f(x1,x2)=min{x1,x2}
suppose a firm's production function exhibits constant returns to scale and that it is making positive profits in equilibrium what would happen to profits if it doubled the level of its input usage what does this argument show? why?
profits would also double so the firm was not profit maximizing! in the long-run the only reasonable level of profits for a competitive firm that has constant returns to scale at levels of output is a zero level of profits if a firm tried to expand 1. firm could get so large that it could not operate efficiently and lead to decreasing 2. the firm might get so large that it would dominate the market and would no longer make sense to behave comeptitively-they should influence market price 3.if one firm can do it, any other firm could do it and this would push down price and lower profits of all firms in the industry
how do you calculate revenue graphically ?how do you calculate total costs? how do you calculate profits?
revenue is p*y* the area y*AC(y*) profits are the difference between the two
What are profits defined as? What is an opportunity cost (in terms of wages)
revenue minus costs all factors of production including opportunity costs ex. if someone works for his own firm then his labor is an input and is a cost -his wage rate is what he "would" be getting if he sold his labor on the open market -if you lose your labor, you forgo the opportunity to use it somewhere else so lost wages are part of the cost of production
how do you solve for the equilibrium level of production assuming perfectly competitive market
set P=MC
What price will the monopolist charge for its product? (*what equation)
set marginal revenue equal to marginal cost
what is the least amount of profits a firm can make in the long run? why is this(think firm choice)? what about the short run
since all factors of produciton are variable in the long run, a firm is alwyas free to use zero inputs and produce zero output in the short run a firm is obligated to employ some factors even if it decides to produce zero output, so it is possible to have negative profits in the short run
What is the slope of the isocost curve? what is the slope of the isoquant? what is the tangency condition for cost minimization? (i got this so wrong the first time lol)
slope of the isocost curve= -w1/w2 slope of the isoquant curve = -MP1/MP2 (TRS) slope of the isoquant must be equal to the slope of the isocost TRS=-w1/w2 technical rate of substitution must equal the factor price ratio
What is the slope of the isoprofit curve?
slope=w/p
what is the supply curve?
supply curve is the part of the marginal cost curve that is upward sloping
calculate the marginal cost of y c(y)=y^2+10
take the derivative of the cost function MC=2y
finding producer surplus (in terms of revenue and variable costs and how to find)
the area to the left of the demand curve PS=revenue-variable costs revenue box- subtract area under marginal cost curve (variable cost)
calculating the change in producer surplus
the change in profits since fixed costs don't change
In the long run, a firm is free to choose... what does the value of the marginal product equal (pMp)
the level of ALL inputs! pMP1=w1 --> the value of marginal product of factor one equals the price of factor one
define short run cost function vs long run cost function (same defintion with adjustment)
the minimum cost to produce a given level of output, only adjusting the variable factors of production minimum cost of producing a given level of output,
what relationship do conditional factor demand functions measure? (think between 2 and 1) explain the difference between conditional factor demands (for a given) and profit-maximizing factor demands (for a given)
the relationship between the prices and output and the optimal factor choice of the firm, conditional on the firm producing a given level of output y condition factor demand-gives cost minimizing choices for given level of output factor demand-profit maximizing choices for a given price of output
define isoquant (set of all combinations of..)
the set of all combinations of inputs that produce a given level of output
long run costs vs short run cost curves...what must be at least as large as the other ...why? when are they the same
the short run cost must always be at least as large as the long run cost to produce y because in the short run a firm has a fixed size while in the long run the firm is free to adjust -firm must be able to do just as well by adjusting the factor as by having it fixed -at y* the long-run and short run costs are the same
price equals marginal cost is a necessary condition for profit maximization but is not a sufficient condition..why?
there may be several levels of output where price equals marginal cost but graphically the profit-maximizing quantity must lie on the upward sloping part of the marginal cost curve -
how do firms pick which set of inputs to actually use? (think what is the goal of firms)
they maximize profits
calculate average cost function c(y)=y^2+10
to calculate the average cost you divide the cost function by y AC= (y^2/y)+10/y= y+10/y
what does the area under the marginal cost curve give? why?
variable costs the marginal cost curve measures the cost of producing each additional unit of output -of we add up the cost, we will get the total costs of production except for fixed costs
what are costs that change when output changes? Write out the Total costs of a firm
variable costs c(y)=cv(y) +F
what does returns to scale describe
what happens to output when you increase all inputs
when the AVC is increasing-describe why the marginal cost curve is where it is
when average variable cost is increasing, for each additional unit of output in, must be adding a number larger than the average cost to the total cost so the marginal cost is greater than the average variable cost
What are the possible profits for the firm in the short run (in terms of price and AC(y*))
zero profits p=AC(y) Positive porifts p*> AC(y*) Negative Profits p*<AC(y*)
Find net profit at the equilibrium level of production
π = py − c(y) where y is found by setting MC=p
