representative household maximise expected lifetime utility \begin{equation} \label{eq:household_utility} E_t \sum_{t=0}^{\infty} \beta^t U(C_t, N_t) \end{equation} where $\beta^t$ is an exponential discount factor and $C_t$ is a consumption index given by \begin{equation} \label{eq:household_C_t} C_t = ( \int^1_0 C_t(i)^\frac{\varepsilon-1}{\varepsilon} di)^{\frac{\varepsilon}{\varepsilon-1}}) \end{equation} $C_t(i)$ represents the quantity of good $i$ consumed by the household in period $t$. Assume there exist a continuum of goods represented by the interval [0,1]. Household maximises (\ref{eq:household_utility}) with respect to the budget constraint given by \begin{equation} \label{eq:household_budgetconstrained} \int^1_0 P_t(i) C_t(i) di …show more content…
Letting aggregate output be defined as $Y_t = ( \int^1_0 Y_t(i)^\frac{\varepsilon-1}{\varepsilon} di)^{\frac{\varepsilon}{\varepsilon-1}})$, it follows that \begin{equation} Y_t = C_t \end{equation} for all $t$. Then, combining the goods market market clearing condition with the consumer's Euler in equation (\ref{eq:eulerequationc_t}) yields, \begin{equation} \label{eq:household_y_t} \widehat{Y}_t = E_t \{\widehat{Y}_{t+1}\} - \frac{1}{\sigma} (r_t - E_t\{\pi_{t+1}\} - r^n_t)\end{equation} natural interest rate is described as \begin{align*}r^n_t = \sigma \frac{1+\varrho}{\sigma + \varrho} (z_{t+1} - z) \end{align*} \subsubsection*{Dynamic IS} Rewriting (\ref{eq:household_y_t}) in terms of output-gap yields the first key equation in describing the model, referred to as Dynamic IS equation (DIS). \begin{equation} \label{eq:household_DIS} \widehat{Y}_{gt} = {\widehat{y}_{gt+1}} - \frac{1} {\sigma} (r_t - \pi_{t+1} - r^n_t) + d_t \end{equation} where I add an exogenous demand shock $d_t$ which follows an AR(1) process: \begin{align*} d = \rho_d d_{t-1} + \epsilon_d
Although it is very close, this combination of TV’s and refrigerators will not fit in the truck. Therefore, the statement is false.
I am following up with you for the supply order. Please forward an approved RSS from Lynn Ellington, and supporting documentation (Pictures) of the items that need to be purchased. I will request the supplies to be delivered directly to museum addressed to you; however, to make the process successful, once the supplies have been delivered, please send me an email confirmation verifying the items in the box with a scanned packing slip for my records. – Thank you
Here we have plugged in the values into our formula. When solving we do order of operations first and we will solve exponents first.
We simply represent all the nodes by $D_i$ for $ 1\le i \le D_\mathcal{D}$ and $Y_k$ refer as the transmission probability gain of the node $D_i$ and $H$ is defined as the total weight. Given the contact rates and the transmission probability gain, $Y_k$ for $ 1\le i \le \mathcal{D}$, and $H$ can readily be computed. As $Y_k$ are continuous-valued real numbers, we need to quantize these transmission probability gain to run the dynamic optimization procedure i.e.,
Secondly, when n=2^(k+1), where k is a nonnegative Integer, we have F(2^(k+1) )≤4*F(2^k )+2^(k+1). We can prove that the function F(n) satisfies the propertyP: ∀k∈N,F(2^k )≤4^(k+1)*F(0)+S_k, where S_k is the k^th term of a sequence of integers 〖(S_m)〗_(m=0)^(+∞) that we will calculate later:
In the unit, called cookies, I have come across many mathematical concepts when doing the math problems. Inequalities were one of the concepts. Inequalities are the relation between two equations that are not equal. One of the first things that were done was to guess and check using random numbers to find the highest number of combinations that would still make the inequalities true. Also, in this unit it reviewed how to place inequalities on number lines; the open circle in inequalities represents greater than or less than and the closed circle in inequalities shows that it is either greater than or equal to or less than or equal to.Another mathematical concept is Systems of Equations. Systems of Equations are equations you deal with altogether
How can we create a model farm out of the materials we are given and explain how a farm works all while using math?
If we clearly view the problems we can see that the problem A is faster, then B. The reason is A have a clear end and it takes few steps to reach it, but problem B have almost unlimited values and it takes a huge time to reach there. This is the reason A is much faster then B. Let’s figure it out mathematically.
Select one (1) company or organization which utilized hypothesis test technique for its business process (e.g., whether or not providing flexible work hours improve employee productivity.) Give your opinion as to whether or not the utilization of such a technique improved business process for the selected company or organization. Justify your response.
This week, many topics have been discussed in class with the importance of understanding context and analyzing visual texts. On Monday, in a class discussion we read a letter from Jourdon Anderson and looking at five different cereal boxes. The letter was from an old servant, provoke the Colonel. The former “employee” Jourdon to come back and work. Instead of accepting the opportunity, Jourdan decline the offer. He didn’t want to come back to work, because he is worried for his children’s safety. Even though, he doesn’t have a good life. He rather be where he is at right now and not moving to where his former employee at. The way he talks about his life, his jobs, his family, and how he appreciated the offer is different many other letters. The reader can imagine Jourdan’s feeling, emotion when he wrote the letter, and by the words he used. The reader can imagine how his former employee will feel when he read the letter. Remember when the time I was beaten until you bowed down on my feet and pray to live? I find that this letter is very interesting.
∆n Sn (d − 1 − r) + (1 + r)Vn pVn+1 (H) + q Vn+1 (T ) ˜ ˜ Vn+1 (H) − Vn+1 (T ) (d − 1 − r) + (1 + r) = u−d 1+r = p(Vn+1 (T ) − Vn+1 (H)) + pVn+1 (H) + q Vn+1 (T ) ˜ ˜ ˜ = pVn+1 (T ) + q Vn+1 (T ) ˜ ˜ = Vn+1 (T ).
The new audio greeting message affects the demand for greeting cards. The demand for greeting cards decreases because greeting cards and audio greeting cards are substitutes. The demand curve for greeting cards pads shifts leftward, from D0 to D1 in Figure 4.6. Simultaneously the fall in the cost of producing a greeting card affects the supply. The fall in the cost of producing greeting cards increases the supply and the supply curve shifts rightward, from S0 to S1 in Figure 4.6. At the initial price of a greeting card, $5.00 in Figure 4.6, there is a surplus of 60 greeting cards per week. The surplus forces the price lower, so the equilibrium price of a greeting card
The 2015 Matriculation Convocation was held at 11:00am in the Murphey Fine Arts Center. As students entered the theatre, they were greeted with a musical prelude by Dr. Samuel Springer. As he played a beautiful melody on the organ, professors, and faculty ushered in wearing their decorated and highly esteemed robes. Once everyone was seated, they were invited to stand for the invocation, presented by Reverend Bernard Keels. Dr. Francis Murphey Draper then greeted all in attendance as well as paid special tribute to the President of Morgan State University, Dr. David Wilson. Following the greeting, Dr. Eric Conway, Conductor, introduced the choir, which sang a beautiful musical selection. Dr. Gloria Gibson then stood to introduce Dr. David Wilson. She spoke on his accomplishments within the educational institution and community. Dr. Wilson proceeded to deliver an amazing speech on the importance of Morgan State University, education,
The economic variable Y is affected by not only the value of X at the same time t but also by its lagged values plus some disturbance term i.e.X_t,X_(t-1),X_(t-2)…..,X_(t-k),ε_t.this can be written in the functional form as:
The above equation is an autonomous linear functional differential equation for $fcircphi_{t}$. Such equation has a solution $fcircphi_{t}=exp(tV)circ fcircphi_{t}$ as $phi_{0}=id$