Econ 115 Midterm 2
Tina makes socks from labor (L) and machines(capital, K). The price of capital is r and the wage of labor is w. Suppose that Tina's production function isQ = 6sqrt(l*k)which has the marginal products MPL = 3√K/√L and MPK = 3√L/√K Show that the ratio of L to K used by Tina depends only on the ratio of the cost ofcapital to the wage; it does not depend on the number of socks that Tina produces.
(maximizes profits) MPL/MPK always= K*/L*= always equals w/r
Shutdown profit/loss=
-FC
Now find marginal Revenue given P(Q)=12-2Q
12-4Q
Suppose that GUESS WHAT Quantities: 1,2,3,4,5,6,7,8 have average costs of 18,16,12,10,15,22,24,29 (numbers correspond to one another), if inverse demand function is P=70-q, how many firms will be in the industry long term?
15 note: Q=q*n (N being firms).
Suppose a firm has two marginal costs, marginal accounting and marginal opportunity costs which both equal Q, what is the firms general marginal cost?
2Q
K stands for
Capital
What is the relationship between Marginal Cost and Average Cost curves:
If MC is below AC, then AC is falling. If MC is above AC, then ACis rising. (2) MC crosses AC at AC minimum
Pareto inefficient
a point that wastes the resources a society has that could make two or more parties happier without making someone unhappier
Pareto dominates when
allocation of resources A dominates allocation B if in moving from A-B but no one can be less happy through a change in allocation
when on Pareto frontier you
are Pareto efficient
MC(Q*)=AC(Q*) and this means that Q* is always ______ this is a very attractive property of_____________
at the minimum of average costs, Perfect competition market
taxes can be used to
avoid negative externalities from occurring
Market for corn is
essentially perfectly competitive
When there are losses?
firms exit, price goes up, erodes losses
Excludable good
individuals can be kept from consuming it
everything to the southwest of a point (on a graph)
is Pareto dominated by the point
Everything to the northeast of a point (on a graph)
is Pareto dominating that point
Beyond Pareto frontier is
literally impossible to achieve
trades are good unless
there is a good ol externality
To what level will a monopolist produce? and why?
when MR=MC this is the point when revenue is maximized
Rival good is
when consumption affects other persons consumption
to what level will a perfectly competitive firm produce? Why?
when p=AC Because they want to break even in the long run (including fixed costs)
Suppose two people don't know each other (or don't know each others preferences enough to swap). What mechanism can you think of that would help them obtain the Pareto Efficient allocation?
A market! If there was a market, prices would emerge that would facilitatePerson A selling their pasta and buying potatoes and person B selling their potatoes and buying their pasta.
Second welfare theorem says
Pareto efficient allocation in perf competitive market is only the initial allocation (governments can reallocate resources for equity and whatnot for new Pareto efficient)
The first wealth fare theorem of economics says
Pareto efficient if all markets were perfectly competitive
when within Pareto frontier
Pareto inefficient
What is the relationship between Marginal Cost and Average Variable Cost curves
(1) If MC is below AVC, then AVC is falling. If MC is above AVC, then AVC is rising. (2) MC crosses AVC at AVC minimum.
Suppose that Tywin Lannister is the only person capable of selling gold in Westeros, the marginal cost of mining each pound of gold is $70. He then turns around and sell his gold for $300 a pound. What is Tywins market power in the gold industry? What is the consumers price sensitivity?
(300-$70)/300=76%,.76 (Market power) Consumer price sensitivity= .76=1/x=.76x=1, 1/.76=1.31 (market power is inverse of price sensitivity)
Define a Monopoly
A market where there's only one seller in the market
Pegovian tax
A tax which raises revenue and social surplus by reducing negative externalities, you want tax to make firm produce at D=SMC
The relationship between Average Variable Cost and Average Cost curves
AC greater than AVC, As quantity increases, the two curves come closer together. (because fixed cost reduced over greater quantity)
Paretto Efficency is
An allocation of resources, what firms produce, how they produce these products, who consumes what
Sunk Costs
Costs that are unrecoverable even if the firm shuts down
With Free entry
Economic ECONOMIC not Accounting profits are driven to 0
EMC is
External MC
A and B are two people who are purchasing a widget in a perfectly competitive industry. Theyhave willingness to pay as follows wtpA > wtpB > ppc where ppc is the perfectly competitiveprice. A widget-maker successfully lobbies the government to introduce regulations that banall producers. The price changes to pm such that wtpA > pm > wtpB . Are the following true or false? Consumer A is not made worse off by the move to a monopoly Consumer B is not made worse off by the move to a monopoly
False. Under Perfect competition, Consumer A received wtpA−ppc. UnderMonopoly, Consumer A received wtpA −pm. As pm > ppc, the consumer surplus forconsumer has fallen and the consumer is worse off. False. Under Perfect competition, Consumer A received wtpb −ppc. UnderMonopoly, Consumer B does not purchase the product (as their willingness to payis less than the price) and so receives a consumer surplus of zero. This is less thanthe surplus they received under perfect competition and so they are made worse offby the move to monopoly.
when there are profits?
Firms enter, price goes down, profit erodes
Show that the allocation of goods across consumers in a perfectly competitive equilibriumleads to 'exchange efficiency'. That is, that there is no possibility for Pareto-Improving tradesbetween consumers. Note, this is essentially asking you to walk through the steps taken inour lecture. In your answer you can focus on the case where there are two goods and two consumers
First understand that to have a Pareto improving trade MUa>MUb, and MUa^2=MUb^2 (one person better off no one worse off) Now understand that mr. ^2 must have trade be so that 0=MUa^2-MUb^2 and MRS blank> MRS^2 HOWEVER we know that in a perfectly competitive market MRS blank =p1/p2 and MRS ^2= p1/p2 So MRS^2=MRS blank So these facts prove that there are no Pareto improving trades with goods bought in perf competitive market.
the MC is almost always upward sloping, this implies that
Increasing production in one factory and decreasing it in another would raise total production costs in the market
Price inelasticity of demand is
L = (changeQ/changeP) (P/Q)
How do we measure a monopolists power?
Lerners index: (P-MC/p) seeing by how much price exceeds marginal cost, also equals (1/AbS(elasticity of demand).
Optimal input approach means that
MCL=MRPL
expressing for marginal revenue is
MR= P2+(change in revenue/change in quantity)*Q1
Optimal output approach
MR=MC of Production
Demand curve in a perfectly competitive market
MR=demand
What is the marginal rate of substitution?
MU1/MU2=p1/p2
Moving along Pareto curve
Makes someone worst off, can't make one better off without making someone worst off if the utility is already on the Pareto frontier
Difference between marginal cost and AVC curves
Marginal cost curve measures the additional cost of producing one more unit while AVC is the average cost of labor per unit produced over Q So BIG Difference and MC runs the show on them graphs
Total revenue=
P*Q
Shutdown Choice inequality
P*Q*>VC (Operate) P*Q*<VC (Shutdown)
compute the exact value of the long run equilibrium price in a perfectly competitive market when all firms have this same cost function. How much will each firm produce? given:TC(Q) = 300 + 3Q^2 is Total cost function hint:derive MC if necessary
P=60
In a competitive equilibrium, all firms produce the quantity that
P=mc
Pareto efficient is when
No feasible allocation Pareto dominates a point on the graph, (Cant make someone better off without making someone else worst off)
holding total inputs constant....
No reallocation of inputs across firms that reduces costs
If you buy food in a perf competitive market, is there a trade that can make two people better off?
No! because they would've already maximized their utilities by buying things in the market for the same prices
Can you reallocate production in a long run equilibrium market even if one firm can produce more at a lower marginal cost?
No, because that firm is already producing at a rate where AC=P, to produce anymore would raise the production cost and thus prices, note the first firm is producing at the same AC in this scenerio as the more efficient company
Do fixed costs factor into the shutdown decision?
No, cause the fix cost would be lost whether or not the firm runs or shuts down
If firm in pc charges more than P they will sell
Nothing
But to Pareto improve
One person must be better off without someone not being worst off
If a point is Pareto efficient it doesn't necessarily
Pareto dominate all points within Pareto curve
Short-run formal definition
Period of time when one or more inputs of production cannot be changed
Non rival+ Nonexcludable is
Pure public good
To find Average ANYTHING divide by....
Q
Optimal input approach and optimal output approach should yield the same....
Q*
Now solve for Tina's choice of K as a function of r, w, and Q (you'll need to manipulatethe production function and substitute it into what you have derived in part (a) of thisquestion). This is called the "conditional input demand function"- the "conditional"references the fact that this is the demand for capital conditional on how many socksTina is producing. Does Tina's demand for K increase or decrease as w increases,conditional on Q?
Q/6*sqrt(w/r)
Whats the difference between Q and q?
Q:market quantity q:firm quantity
Now find profit maximizing quantity and price
Q=2, P=8
Study Break
Second Welfare theorem not on the exam!
when MC<AC then
Supply curve quantity is a 0
What is the substitution effect?
a change in relative prices
The Marginal Revenue Product is
The increased revenue from one additional labor unit input
P=AC what does this mean?
Then market is in equilbream
So in perf comp market
There are no Pareto improvements that can be made
What are the problems with Social Surplus as a measure of welfare? How does the concept of Pareto efficiency improve on them?
There are two problems with Social Surplus. The first is that it does not take into account distribution of welfare. It ignores how consumer surplus is distributed across consumers or producer surplus across producers. In particular, consumer surplus depends on the willingness to pay. Rich people have a higher willingness to pay then poor people, even though they don't necessarily derive higher utility from the product. The second problem is that social surplus focuses on one market at the time, ignoring the effects on the economy at large. Therefore, the social surplus measure may overstate the welfare generated by this market. A Pareto improvement occurs if some people are better off after some change, but no one is worse off. A Pareto-efficient situation occurs when all possible Pareto improvements have been made, and no further Pareto improvements are possible. Pareto improvements are desirable because, by definition, some people are better off, and no one is worse off. But a Pareto-efficient allocation may still not be a desirable situation. Like the social surplus, Pareto efficiency does not take fairness, or equity into account.
MR of monopolist is
U shaped (Upside down)
X and Y axis of a Pareto efficient are measured in
Utils
The first wealth fare theorem of economics is
What firms produce, how they produce these products, who consumes what.
Short-run often means
When profits or losses exist in a perfectly competitive market
Will outcome be PE if all markets were perfectly competitive?
Yes
MR can also=
change in total rev/change in quantity
An isoquant is a curve representing....
combinations of inputs that allow a firm to make aparticular quantity of output.
neg externality
cost imposed on some who aint got nothin to do with the damn transaction
Externality
cost or benefit affecting party not involved in transaction
Monopolists face a downward sloping
demand curve
SMC is
different from mc
Supply curve of a PC FIRM is
the part of the MC curve that's above/at the AVC curve
Draw a (large) graph. On your graph draw the following:i. Demand Curve (D)ii. Marginal Revenue Curve (MR)iii. Average Costs (AC)iv. Marginal Costs (MC)
n/a
On your graph mark the monopolist's optimal price (P∗m) and quantity (Q∗m). Indicate the monoplists' profit and the DWL of monopoly on your graph.
n/a
with Pareto efficency
no waste of potential opportunities (can't make something better without making one worst off)
in perfectly competitive market chosen X1,X2 such that MRS=.... so in perf MRSa=MRSb
p1/p2 (Price ratio)
Firms always choose that
p=MC(q*)
When Market perfectly competitive
production at minimum AVC (in the long run)
Given: TC(q) = 10 + 2q2 and P=20 and MC=4Q Find Profit and is the market in long run equilibrium
profit=40 Not in long run equilibrium since the firm is making a profit, so free entry and exit process has not yet driven profits to 0
To get market equilibrium
set dem=MC
to get social optimum
set dem=marginal social cost MSC=MS+neg externality
Neg externality graph
surplus all over but area between SMC=MC+EMC is negative surplus (the externality)
Income effect is
the change in someones spending habits as a result of their purchasing power increasing
