Econ 203 Remaining MQ and Q
Investing costs either person $10. The returns to investing are split equally, regardless of who invests. If no one invests, the returns are $0. If one person invests, the returns are $10, so each gets $5. If both invest, the returns are $24, so each gets $12. The payoff matrix is: The example is:
(Prisoner's Dilemma or a Commitment problem) This is an example of a Prisoner's Dilemma, part of a broader class of strategic games called commitment problems. In the Prisoner's Dilemma, the only Nash Equilibrium is for both players to defect (or shirk, backstab, etc) even though cooperating gives them both higher utility.
Suppose the demand curve for apples is given by Q = 40/P - 5. What is the price elasticity of demand for apples when the price is 4?
-2, The elasticity is given by: dQ/dP * P/Q. dQ/dP = -40/(P2) e = -40/16 * 4/5 = -2
Suppose there are 2 goods, x & y, and we have a graph of Bob's indifference curves in the (x,y) plane. Suppose a segment of Bob's price-consumption curve of good x is perfectly horizontal. What must be true?
-Bob buys no more or less of good y as the price of x increases -The fraction of Bob's income spent on x, (xpx) / m, is constant. -Bob's demand curve for good x is unit elastic (elasticity of -1)
Which of the following are the assumptions of perfect competition?
-Individual firms (and individual consumers) have no influence over the market prices of goods. -All firms in an industry sell an identical, standardized product. -Firms and consumers have perfect and complete information about all goods. -In the long run, there is free entry and exit to all industries.
In Rye, NY, there was a small amusement park called Playland that charged both an admission fee (in the form of a parking fee) and a price per ride (in the form of tickets that had to be purchased.) Why might Playland have implemented this two-tiered pricing scheme?
-It allows Playland to capture more consumer plus for itself. -Charging for individual rides allows the park to ration rides better than a waiting line would, and allows to park to more accurately recoup operating expenses specific for each ride. -The scheme yields higher profits than a simple admission fee or ride tickets alone.
What is true (and false) about the Bertrand Model of duopoly for two firms with identical, upward-sloping marginal cost curves?
-It assumes consumers have perfect, free information. -it assumes both firms make their pricing decisions simultaneously. -It concludes that the price and quantity are equal to the perfectly competitive outcome. -It concludes that the price each firm chooses will be equal to its marginal cost.
What is true (and false) about the Cournot Model of duopoly, where the two firms have identical, constant MC curves?
-It assumes that both firms will price their good identically, at whatever price the market will bear at their combined level of output. -It assumes that the two firms choose their quantity of output simultaneously. -It assumes that the firm's goods are perfect substitutes. -It concludes that the two firms combined supply a greater quantity than a monopolist would.
Which of the following is a commitment device that will guarantee that both people with invest? (Make Invest, Invest the only Nash Equilibrium?) (Check all that apply.)
-The government taxes both individuals $10 and makes the investment itself. -Both sign a contract that if one person doesn't invest and the other does, the non-investor pays the investor $6. -The government imposes a penalty of $6 on anyone who doesn't invest
Suppose John has an online business in addition to his job, and he can decide how many hours per week to spend working on it. Any time he doesn't spend working on his business can be spent working overtime for $30/hour. The accounting profit (not including opportunity costs) of his business is a function of how much time he spends on it: 1 hour: $10 2 hours: $60 3 hours: $110 4 hours: $150 5 hours: $185 6 hours: $210 7 hours: $200
-The marginal benefit of the 3rd hour is $50 -The marginal benefit of the 4th hour is $40 -The average benefit of working 4 hours is $37.50 f. John should spend 5 hours working on his side business because the marginal benefit of the 5th hour is greater than $30, but the marginal benefit of the 6th hour is less than $30.
Which of the following are characteristic of a monopolistically-competitive industry?
-brand loyalty -differences in quality between firms' products -product differentiation due to advertising -imperfect substitute goods -free entry & exit
The marginal revenue of a firm under perfect competition is:
-equal to the market price, P*, for every unit sold -graphically, a horizontal line -set equal to the firm's marginal cost to find the profit-maximizing quantity, Q*
The marginal revenue of a monopoly firm is...
-set equal to the firm's marginal cost to find the profit-maximizing quantity, Q* -less than the price consumers are willing to pay for that unit -graphically, a downward sloping line -sometimes negative
Each point along the market demand curve for a good shows:
-the relationship between the amount (quantity) of the good and the price consumers are willing and able to pay for that amount. -how much of the good that consumers would be willing and able to purchase at any price
The short run marginal cost is...
-the slope of the short run total cost function at that output -the wage rate times the additional labor needed to increase output by one unit
Which of the following utility functions represent the exact same preferences as the utility function u(x,y) = 2x + y ?
-u(x,y) = 6x + 3y -u(x,y) = 2x + y - 7 -u(x,y) = ln(2x + y) -u(x,y) = (2x + y)^3
The demand function is P = 850 - 20Q. If a monopoly's marginal cost is 50, what is the monopoly's optimal equilibrium quantity if it is optimal for the monopoly to produce?
20
Suppose, as in Question 5-7, a firm's production function is 2*K^0.5L^0.5, and in the short run, capital is fixed at K0 = 400. What is the firm's short run average product of labor function?
40/(L^0.5)
Suppose a firm's production function is 2*K^0.5L^0.5, and in the short run, capital is fixed at K0 = 400. What is the firm's short run production function (aka, short run total product of labor)?
40L^0.5
quiz 3, #2, d
A Giffen good is one which you buy less of as its price falls. Bob buys more x as px falls.
what is a normal good?
A normal good is a good that consumers will buy more of as their income increases. (ex. steak)
what does each point on the on the 5 different indifference curves mean?
Each point maximizes Jenny's utility subject to a different budget constraint. All of the budget constraints have the same slope, -px/py, but different levels of income. Maximizing utility means setting MRS = du/dx / du/dy equal to px/py. Graphically, this means the slope of the indifference curve equal to the slop of the budget constraint. Since the price ratio is the same at all 5, her MRS is the same at all 5.
what is the difference between economic cost and accounting cost?
Economic cost is the sum of explicit cost and implicit cost. Implicit cost here is considered as opportunity cost. On the other hand, accounting cost is only explicit cost
Why is the above points correct in regards to why Playland may have implemented a two-tier pricing scheme?
Even though it may seem like businesses are profiting at the expense of consumers, this is often not true. Yes, they are increasing their profits, but "tiered-pricing" mechanisms can actually increase the utility of consumers by letting people use a good at different "levels," and bring us closer to a state called Pareto Optimality (no forgone opportunities, no deadweight loss) when markets are not simple (natural monopolies, asymmetric information, transaction costs, incomplete contracts).
If the average cost of producing a good is increasing as a firm produces more of the good, then which of the following must be TRUE?
All of the above
When we can't know utility functions:
All we get to observe is how much stuff people buy, (x, y), under given prices & income, (px, py, m), and the rational choice model lets us explain this phenomena.
Isoquant
An Isoquant is a curve that shows the set for all pairs of inputs that yield the same level of output (iso denotes constant, and quant means quantity)
What is an indifference curve?
An indifference curve shows a set of consumption bundles among which the individual is indifferent. That is, the bundles all provide the same level of utility.
u(x,y) = x^a * y^b
Cobb-Douglas, preferences are preferences for which the consumer spends the same percentage of his income on x (and y) regardless of the values of px, py, & m. In particular, px*x/m = a/(a+b) and py*y/m = b/(a+b).
What does the "convex" mean? And how is it related to indifference curve?
Convex Assumption: "Average is preferred to the extreme"
"A profit-maximizing firm will produce at the output level where average revenue equals average total cost."
FALSE
"Considering the short run, average variable costs and average total costs are minimized at the same output level."
FALSE
"Profit is maximized at the output level where average cost is minimized."
FALSE
Explain the law of diminishing marginal product.
Fall in the rate of increase in output as the amount of an input (for example, L) is increased, while holding the other input factor (for example, K) constant.
What is the dead weight loss because of inefficiency of exercising monopoly power?
In order to calculate the dead weight loss by monopoly power, you need to calculate the total surplus (consumer surplus + producer surplus) under the situation of perfect competition.
"Assuming they have the same production function, and face the same input prices, w & r, the long run average cost curve is the same regardless of whether a firm is a monopoly or perfectly competitive."
True
"Assuming they have the same production function, and face the same input prices, w & r, the long run expansion path (the cost-minimizing L & K for any amount of output, Q) is the same regardless of whether a firm is a monopoly or perfectly competitive."
True
"Assuming they have the same production function, and face the same input prices, w & r, the profit maximizing output, Q*, is the same regardless of whether a firm is a monopoly or perfectly competitive."
True
"Average total cost reaches a minimum at the output level where average total cost equals marginal cost."
True
"In the long run, free entry and exit will cause the price of the firm's output good to approach the minimum value on its average total cost curve."
True
"In the short run, a firm may choose not to shut down even if total revenue is less than total costs at every output level."
True
"Output levels (values of Q) where the Demand curve is inelastic (0 < |e| < 1), can never be profit-maximizing to a monopolist."
True
"Profit equals zero at any output level where price equals average total cost."
True
If supply increases and demand decreases, equilibrium price will fall.
True
In the long run, a firm in a monopolistically-competitive industry will face a demand curve tangent to the downward-sloping portion of its average cost curve.
True
In the long run, a firm in a monopolistically-competitive industry will have zero economic profit.
True
Match each aspect of consumer theory to its analogue in producer theory.
Utility function=Production function Utility maximization=Cost minimization (MRS)Marginal Rate of Substitution=(MRTS) Marginal Rate of Technical Substitution Marginal Utility=Marginal Product Expenditure function (the minimum income necessary to reach any utility value)=Long-run total cost Indifference curves=Isoquants Budget constraint=Isocost line Income-consumption curve=Long-run output expansion path
Are Utility functions ordinal or cardinal?
Utility functions are ordinal, not cardinal. Utility functions only serve to compare bundles of goods, NOT say "by how much more" the consumer prefers one basket over another.
quiz 3, #2, e
We're letting px vary. So the demand curve for y is shifting. Thus, we're not even talking about one lone demand curve for y, so this option makes no sense
What are opportunity and sunk costs?
Opportunity costs are the costs of engaging in one activity instead of another, while sunk costs are costs incurred regardless of which activity you choose. When making decisions it is absolutely important to consider what you will be giving up— the opportunity cost. If some costs are the same regardless of what you do — sunk costs, these costs are irrelevant.
How much is the total cost?
TC = ATC * Q, where ATC on the graph for the amount of Q
How much is the total revenue?
TR = P*Q
When the marginal product curve lies above the average product curve...
The average product curve must be rising.
Show the optimal choice of the consumer for the case of convex preferences..
The choice is where the indifference is tangent to the budget constraint. That is, maximize utility with respect to (or subject to) budget constraint
What does the demand curve show?
The demand curve shows the relationship between quantity and the price consumers are willing to pay for that quantity, and also the quantity of a good consumer are willing to pay at each price. It holds consumers' incomes, the quality of the good, population, time, and everything else constant.
"The supply curve of the firm is the part of its marginal cost curve that is upward sloping and lies above the average variable cost curve".
The firm's short-run supply curve shows how much it will produce at a various possible output prices. That is, the short-run supply curves is the relation between price and quantity supplies which 7 satisfies the first rule for SR profit maximization (Marginal output rule) and the second rule for SR profit maximization (No shutdown condition).
Suppose that you are the manager/head mechanic of a small auto repair business. Suppose that if you work alone, you can fix 2 cars in a week. If you hire a second employee, the business can fix 5 cars per week. Three employees, 9. Four employees, 12. Five employees, 13. Six employees, 11. At how many employees did diminishing marginal returns set in?
The fourth employee because the increase in number of cars fixed with hiring the fourth is less than with hiring the third.
What is the income-consumption curve?
The income-consumption curve is the set of points (bundles of goods x & y) which Jenny buys for every possible level of income, m, holding the prices of x & y constant.
Which following curve makes an increasing-cost industry?
The industry's long-run supply curve.
What is an equilibrium price?
It is the one where the amount demanded equals the amount supplied.
What is the comparative statics?
It is the study of how the equilibrium price and quantity change when the underlying conditions change.
What is the demand curve?
It measures how much people wish to demand at each price.
What is the supply curve?
It measures how much people wish to supply at each price.
Consider the production function Q = K^1.5L^0.5 where K is capital and L is labor. What is the marginal rate of technical substitution for this production function?
K/3L
In the short run, what is the desired level of output that this firm will choose?
MC = MR is the general condition to find the optimal Q*. But, we know that the perfectly competitive firms follows MR = P. Therefore, eventually we have MC = P.
What is the optimal level of output for a monopolist?
MR=MC, so find mc by finding the derivative of Cost and setting it equal to MR or the demand(x2 slope?)
Can two indifference curves cross each other?
No
Suppose there are only 2 goods, x & y. Is it possible for both to be Giffen goods simultaneously?
No, If a good is Giffen, you buy fewer units of it if your income increases, holding the prices fixed. If both goods were Giffen, it would mean you are buying fewer units of both, so spending less on both, meaning you are not spending all of your income.
Suppose the price of x falls. If x is a ____ good, the ____ effect on x will be...
Normal, substitution=positive Inferior, substitution=positive Giffen, substitution=positive perfect complement, substitution=zero Normal, income=positive Inferior, income=negative Giffen, income=negative perfect complement, income=positive
"Bob buys no more or less of good y as the price of x increases" is true.
The price-consumption curve shows the optimal (x,y) bundles as px changes, holding py & m fixed.
MRS
The slope of the indifference curve is called the marginal rate of the substitution. The name comes from the fact that the MRS measure the rate at which consumer is just willing to substitute one good for the other.
technical rate of substitution (TRS).
The technical rate of substitution measures the tradeoff between tow inputs in production. It measures the rate at which the firm will have to substitute one input for another in order to keep output constant
So the utility functions u(x,y), u(x,y) + 7, 2*u(x,y), e^(u(x,y)), ln(u(x,y)), (u(x,y))^2, etc all represent the same preferences because:
They all have the same indifference curves
Average cost decreases when the marginal cost is lower and increases when the marginal cost is higher
This is true for any cost that varies with output
What does utility functions being ordinal mean?
This means that utility functions are unique up to any monotone increasing function (Adding/subtracting a constant, multiplying or dividing by a positive number, raising to a positive power, logarithms, exponentiation). All they do is change the utility number value, eg. u(2,3) = 5 vs u(2,3) = 17, assigned to baskets, not the ranking between baskets.
Can whether a good is Normal, Inferior, or Giffen depend on the particular values for px, py, & m?
Yes, A good's "inferiorness" ALWAYS depends on current prices & income. For example, for extremely low levels of income, both x & y must be Normal, for any utility function that satisfies the 4 assumptions in Chapter 3.
In the rational choice model with 2 goods, x & y, and our usual assumptions, given a consumer's utility function, what values need to be known to uniquely predict how many units of x & y he will buy?
You need to know the consumer's income, the price of y and the price of x
Why do economic models make unrealistic assumptions about individual behavior?
a. Even if the assumptions are unrealistic, the conclusions of these models still approximate real-world behavior well. b. Simplifying assumptions can produce easily solvable models. c. Even if the assumptions do not account for all intricacies of human behavior, they are still accurate in many contexts most of the time. d.Even if the assumptions are unrealistic AND the conclusions are not always accurate, useful insights can be gained (for government policy, making better models, etc) by analyzing models of rational decision-making. e. Even if economic models do not always accurately predict human behavior, then can still inform us how to improve our decision-making.
The budget line shows:
all possible combinations of two goods that can be purchased, given money income and the prices of the goods.
When the percentage change in the quantity demanded is less than the percentage change in the price, then:
demand is inelastic
Suppose Carlos has a son, Joe, and has altruistic preferences such that Carlos' utility function is u(C,J) = C4J, where C is his own income and J is Joe's. Carlos makes $10,000 per month and Joe makes $2,000. How much money will Carlos give Joe per month (in dollars)?
du/dc = 4c3j du/dj = c4 MRS = 4j/c = pc/pj = 1/1 = 1 The "budget constraint" if they were to pool their incomes is c + j = 12 (in thousands of dollars), so the price of either Carlos or Joe having $1 is, well, $1. Carlos' income-consumption curve is j = c/4. Solving gives c = 9.6 & j = 2.4, so Carlos will give .4 thousand dollars, or $400.
Do the following production functions exhibit increasing, constant, or decreasing returns to scale?
f(K,L) = sqrt(K* L)=Constant returns to scale f(K,L) = 0.1KL=Increasing returns to scale f(K,L) = 2K + 3L=Constant returns to scale f(K,L) = 3K^0.25L^0.5=Decreasing returns to scale
"Bob's demand curve for good x is unit elastic (elasticity of -1)" is true
his total expenditure on x isn't changing, so elasticity of demand is -1.
Suppose a firm has fixed cost of FC = $450 and variable cost equal to VC = 20Q + Q^2. If the price is equal to $50, how much should this firm produce in the short-run?
mc=20+2Q, p=mc so $50=20+2Q which solved equals to Q=15
The optimal amount of time spent doing some activity is when the marginal benefit is greater than marginal cost, AND the total benefit is greater than the total cost
optimal amount= MB>MC and TB>TC
The rational choice model allows us to:
take prices & income, (px, py, m), along with a given (well-behaved) utility function, and predict a unique basket of goods the person will buy, (x, y).
Short run/long run
we define the short run as a time period over which only one of the firm's inputs is a variable factor while all of the others are fixed factors. In other words, the short run is a time period over which the quantity of one input can be varied, but the quantities of all of the firm's other production 3 factors cannot be adjusted. In contrast, the long run is a time period long enough that all of the factors are variable and none is fixed.
"The fraction of Bob's income spent on x, (xpx) / m, is constant." is true
we know Bob buys a constant amount of y. Also, py and m are fixed. Therefore, a flat PCC means Bob's expenditure on x, xpx = m - ypy, doesn't change. So, (xpx / m) doesn't change.
"sticker-price aversion"
which assumes irrationality on the part of consumers. We want our economic models to explain consumer & business behavior without requiring irrationality.
Quiz 4, #7, A
while the explanation about sunk costs may be convincing, people know ahead of time that they will pay for admission plus ride tickets. The "sunk cost" factor does allow Playland to capture more of consumer surplus as profits via the admission fee, but for anyone whose total benefit of going would be less than the total cost of admission, travel, and ride tickets, they would never choose to have gone in the first place.
If a firm had decreasing returns to scale at all levels of output and it divided up into two equalsize smaller firms, what would happen to its overall profits?
In the case of decreasing returns to scale, it is not a good idea to double inputs because the firm will get less output than just doubling outputs (See the answer 1 from Ch. 18). Therefore, it the firm divides up into smaller firms avoiding doubling inputs, then the firm can secure the profit.
u(x,y) = min{ax, by}
Perfect complements are goods for which x only gives utility when combined with y, so the consumer only ever buys them in bundles with a fixed ratio, regardless of the price ratio. Examples could include peanut butter & jelly, salad & salad dressing, or hot dogs & hot dog buns.
u(x,y) = ax + by
Perfect substitutes, are goods for which a unit of x is equally as good as a unit of y, so the consumer will just buy whichever is cheaper (has a higher marginal utility per dollar). Examples could include Sprite & 7-Up, Exxon gas & BP gas, or eggs packaged in dozens vs half-dozens.
Suppose Jim's utility function over goods x & y is u(x,y) = x + 3y. This utility function exhibits:
Perfect substitution
Finding profit or loss:
Profit (or loss) = TR - TC
What is the total profit (or loss)?
Profit = TR - TC = P * Q - TC
u(x,y) = ln(ax) + by & u(x,y) = ax^1/2 + by^1/2
Quasilinear preferences are ones for which indifference curves are convex, but have potential corner solutions, like Figure 3.16 in the text. Utility functions include
What is a monopolist price?
Set the y found from the optimal level output (mc=mr) and put it in the demand function
Suppose Joe's utility function over income, m, and hours of leisure, h is u(m,h) = m/120 + ln(h). Also, there are 24 hours per day, and he earns an hourly wage w, so his budget constraint is wh + m = 24w. What is the absolute lowest wage for which Joe will work more than 0 hours per day?
Slightly over $5, you can solve this when you realize if Joe does not work, h = 24 & m = 0, so his utility is u = ln(24). You can just find the negative slope of the "u=ln(24)" indifference curve at this point, because MRS = ph/pm = w. (One dollar of income "costs" $1 so pm = 1, and "buying" an hour of leisure means forgoing $w of income, so ph=w). m = 120ln(24) - 120ln(h), which has a slope of -120/h, and -120/24 = -5.
If capital and labor are perfect substitutes in a production function, the isoquants for this function will be:
Straight lines
Find reason why perfectly competitive firms' short-run supply curve is upward sloping.
a and b are correct.
