0
votes
0answers
23 views

How do I express this profit function as a function of prices only?

How do I express this profit function as a function of prices only? The function is $(p-AC)q$, where $p$=price, $AC$=average cost (NOT marginal cost), and $q$=quantity sold. so in numbers ...
1
vote
1answer
48 views

Show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model.

Under the assumptions of the classical simple linear regression model, show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model. Anyone have any ...
0
votes
1answer
15 views

Deriving Stochastic Euler Equation

If a consumer has utility function \begin{equation*} u(c_t) = ac_t - \cfrac{b}{2}c_t^2 \end{equation*} and present value budget constraint \begin{equation*} \sum_{j=0}^\infty E_t[\beta^jc_{t+j}] = ...
2
votes
1answer
56 views

Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
0
votes
0answers
39 views

What quantity should the firm produce if it wants to maximize its profit given short run marginal coast and short run total cost function

A bicycle repair shop charges the competitive market price of 10 dollars per bike repair. The firms short run total cost is given by STC(Q)=$\frac{Q^{2}}{2}$ and the associated marginal cost curve is ...
1
vote
1answer
53 views

utility and uncertainty of economics

United Petroleum is operating a deep water oil rig in the Gulf of Calexico. Management have been informed that the drilling riser may be susceptible to methane build up and hence at risk of an ...
0
votes
0answers
105 views

Computing the certainty equivalent for the lottery of infinite expected value

How can I compute the certainty equivalent for the lottery for someone whose Bernoulli utility function is $u(x)=\frac{x^{1-\gamma }}{1-\gamma }$ where $0< \gamma < 1$? Also, how much would the ...
0
votes
1answer
32 views

Show that there exist prices at which agents can engage in mutually beneficial trades.

Consider an exchange economy with $2$ goods and $2m$ identical Households, but in this case each household has utility function $u(x_1,x_2)=x_{1}^2+x_{2}^2$, and endowments $w_1=w_2$. Show that there ...
0
votes
0answers
108 views

Robinson Crusoe economy problem

Consider the Robinson-Crusoe one-consumer, one-producer economy. Compute the equilibrium prices, profits and consumption when the production function is $f(L)=\sqrt{L}$, the utility function is ...
0
votes
1answer
31 views

Forward contracts

How do I do this one? I'm assuming it's not as simple as "the initial value is just $50 since thats what the stock sells at"
1
vote
1answer
24 views

Constrained optimization when lending money between two periods

The question is: A consumer has utility function $u= x_{11}x_{12}+\beta x_{21}x_{22}$ where $x_{ti}$ is amount of good $i$ consumed in period $t$, $\beta$ is a positive parameter. We are asked to ...
1
vote
1answer
53 views

Math / Accounting problem

I have been stuck for over an hour with the following problem. In my textbook the following is written: "Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 ...
0
votes
0answers
102 views

Question involving theory of the firm

Any ideas on how to help me get started on this question? A firm's technology possesses all the usual properties. It produces output using three inputs, with conditional input demands ...
0
votes
1answer
118 views

Nash Equilibrium in Cournot Duopoly

If you have a demand function Q1= 20 + 3/4 p2 - p1 and Q2= 20 + 3/4 p1 - p2, how does one go about solving for the Nash equilibrium if you know there are no costs? I've tried solving for Q and then ...
1
vote
0answers
788 views

Profit Maximization Question of a Leontief (Perfect Complements) Production Function?

This is a question from my intermediate micro economics text book. Any help is very appreciated! Given Info: Company ST (a company which offers custom travel-planning services) is a ...
0
votes
1answer
206 views

Question related to the General equilibrium in exchange economies

I need some help in solving this question: Consider the following two-person, two-good economy. Persons $A$ and $B$ each consume two goods xylophones $(x)$ and yams $(y)$. Person $A$ enters the world ...
0
votes
1answer
60 views

Density income and Total Income.

Suppose that the density income function is $f(r) = a*exp(r^2)$ with $r \in(0; 10)$ (hundred thousand euros) and $a=exp(10)-1$. Assume that the total number of people in this economy is 1 million. ...
0
votes
1answer
86 views

Production function (economy)

A company produces one good using two factors of production factors. If $x$ and $y$ denotes the units of the factors used by the company, the technology function is given by $F(x; y) = xy^2$. In the ...
3
votes
2answers
218 views

Exercise in Mechanism Design

I found an exercise with solution in the field of Mechanism Design. The problem is I don't understand the solution. Exercise. Use the characterization of incentive compatible direct-revelation ...
3
votes
1answer
119 views

Existence of asymmetric equilibria in the dollar auction game

Consider a game in which an auctioneer sells one dollar to the highest bidder. The high bidder wins the dollar, but every bidder pays their bid. Concretely, assume that there are two bidders ...
1
vote
0answers
159 views

Econometrics Simultaneous equation Indirect Least Squares and Two Stage Least Squares

I still can't figure out this problem. PLEASE HELP! (1) $F_t = a_1 + a_2.C_t + a_3.P_t + e_t$ (2) $P_t = b_1 + b_2.F_t + b_3.S_t + b_4.I_t + u_t$
0
votes
1answer
83 views

Calculating the bank multiplier.

The question is as follows: In a simple close economy, banks are required to maintain a liquidity ratio of 8%. An additional £15 billion of currency is deposited in the banking system. Calculate the ...
1
vote
1answer
11k views

Deriving demand functions given utility

A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$. Derive the ...
0
votes
1answer
128 views

Find profit maximizing profit and quantity given willingness to supply curves and a merger

This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies. Consider a regional market for wholesale electricity where ...
2
votes
2answers
2k views

Cournot-Nash Equilibrium in Duopoly

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question: There are 2 firms in an industry, ...
0
votes
0answers
35 views

Linear Regression for Econometrics

If I am given the line $y_{i}=1+.5x_{i}+u_{i}$ along with 10 observations of some variable X and 10 observations of error terms (pulled from a normal distribution with mean=0 and variance=10) and I am ...
1
vote
1answer
193 views

Normal distribution theoretical moments

how we can show that the following equality holds $E[(x-\mu)/\sigma]=0$ $E[(x-\mu)^2/\sigma^2-1]=0$ $E[(x-\mu)^3/\sigma^3]=0$ $E[(x-\mu)^4/\sigma^4-3]=0$
2
votes
1answer
144 views

vickery auction question(second-price auction)

The question is as follow, Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
0
votes
1answer
227 views

subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
1
vote
2answers
3k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
1
vote
1answer
152 views

Cournot-game problem

I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise: Consider the market for Blue Turtle (a new ...
0
votes
1answer
93 views

question on T period bargaining(alternating offers).

the following question is a kind of Rubinstein bargaining model: 2 players, A and B, have 100dollars to divide between them. They agree to spend T days negotiating over this division. The first day, ...
1
vote
1answer
112 views

Find the real exchange rate

If the nominal exchange rate increases by 5%, while domestic inflation is 2% and foreign inflation is 3% then the real exchange rate changed by?
1
vote
1answer
210 views

Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
0
votes
1answer
83 views

Interpreting an integral/ probability

Think of two iid random variables $x$ and $y$ with density $f$ and CDF $F$ and a constant $c$. What could the qualitative meaning of the following expression be? ...
0
votes
1answer
527 views

bounding the the expected value of the maximum of two random variables

Consider two standardized random variables $x$ and $y$, and define a function $g(x,y)=E[max(x,y)]$ where $E$ is the expected value operator. My question is finding the upper and lower bounds of ...
0
votes
1answer
62 views

what can we say about $G(.)$?

Given $c \in R$, a deterministic probability density $f(x)$ and its cumulative distribution $F(c)$, what can be said about $G(c)$ where: $G(c)=\int f(x)F\left( x+c\right) dx $ The question ...
2
votes
1answer
95 views

Non-core allocations in the 2-fold replica of an economy.

Here's the definitions I'm using, just in case. Let $E$ be the exchange economy given by agents $A,B$, starting allocations $x_A=(0,1)$, $x_B=(1,0)$ and utility functions given by $u_A=x+y$ and ...
0
votes
2answers
617 views

Subgame Perfect Nash Equilibrium

My homework question is summarized below: There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
1
vote
1answer
59 views

Working out interest rates on a futures contract/exchange rates contract.

okay my main problem is I have to work out a $3$ month interest rate for the us dollar. The question I'm stuck on is At the end of trading on $1$ January $2012$ the dollar/pound spot exchange rate ...
0
votes
0answers
62 views

Computing interest rate from investment and return

At the beginning of every year a bank customer deposits v euros in an investment fund and withdraws, at the end of the n-th year, a capital of M euros. We want to compute the average yearly rate of ...
0
votes
1answer
698 views

Finding Nash Equilibria with Calculus

The problem is summarized as: There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
1
vote
1answer
839 views

Unable to find Nash equilibria in mixed strategies

Here is the strategic form game: Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 ...
2
votes
1answer
781 views

How to find Pareto-improvements with maths?

I hope this is not off topic. I've got two utility functions for two different kinds of agents, A and B, and their endowments ($w_1$ and $w_2$) of the (2) goods ($x_1$ and $x_2$). The utility ...
0
votes
1answer
149 views

Finding competitve equilibrium(consumption rivalry)

Consider two agents (Pascal and Friedman) in a pure exchange economy with two goods and no free disposal. Pascal has a preference relation give by the utility function $$u^P(x_1^P,x_2^P)=a\ln ...
0
votes
1answer
107 views

Market optimization problem

Demand schedule: $Q_d=a_0-a_1P_d$Supply schedule: $Q_s=b_0+b_1P_s$$P_d$ and $P_s$ are prices faced by consumers and producers. $a_0,a_1,b_0,b_1$ are all positive constants, where $a_0>b_0$. The ...
0
votes
1answer
844 views

Calculating “deseasonalised sales y” when forecasting 2004Q1-2004Q2

I'm currently having difficulty calculating values for the deseasonalised sales column. How do you go about doing it for 2004Q1-2004Q2? Btw in case you are wondering: $$2004Q1$$ $$First MA = ...
0
votes
0answers
167 views

Understanding a Proof in Probability Theory

My question is pretty simple: I have two equations which are supposedly true (from a published paper) but I have no idea how to arrive at the solution myself. So it would be great if someone could a) ...
0
votes
1answer
459 views

Describe the Engel's curve for the optimum consumption bundle

A consumer has the utility function $u(x_1,x_2)=(x_1^a+x_2^a)^{1/a}$ where $0\neq a<1$. Her expenditure must satisfy $p_1x_1+p_2x_2=I$, where $p_i$ is the price of a good i, and I is her income. ...
3
votes
3answers
771 views

Using the definition of a concave function prove that $f(x)=4-x^2$ is concave (do not use derivative).

Let $D=[-2,2]$ and $f:D\rightarrow \mathbb{R}$ be $f(x)=4-x^2$. Sketch this function.Using the definition of a concave function prove that it is concave (do not use derivative). Attempt: ...