# Tag Info

7

For theory you have in order of prestige... (I know subjective) Journal of Economic Theory Theoretical Economics AEJ-Micro (only micro) Mathematics of Operations Research (OR related) Games and economic behaviour (only game theory) Economic theory Journal of Mathematical Economics Social choice and welfare (only social choice) Theory and Decision ...

3

You have most of this; it seems like you might have a miscalculation when differentiating the fraction: \begin{align*} \frac{dk_t}{dt} = \frac{d\frac{K_t}{N_t}}{dt} & = \frac{\frac{dK_t}{dt}N_t - \frac{dN_t}{dt}K_t}{N_t^2} \\ & = \frac{\frac{dK_t}{dt}}{N_t} - nk_t \end{align*} thus $$\frac{\frac{dK_t}{dt}}{N_t} = \frac{dk_t}{dt} + nk_t,$$ and ...

0

Similarly to what 1muflon said, there's really nothing sacred or true about the Cobb-Douglas production function. It's just a simple function that has some desirable properties. (e.g. that marginal productivities are equal to average productivities.) Things resembling "proofs of the Cobb-Douglas production function" that you might come across will ...

2

Since you have discrete datapoints and want to calculate PED, you will have to make assumptions, like "the data represents the general behavior of the consumption function". (You can also get more data or throw your hands up in despair.) If you know that price has no effect on the quantity demanded, you can apply the PED formula, and get a very ...

3

yes. Notice that a good is normal, inferior Giffen for a certain value of prices/income. For example, a good might be inferior at some prices/income but normal for some other values of the prices/income. In some cases, however, you can make stronger statments. For example, homothetic preferences always lead to normal demands as $$x_1(p_1, p_2,m) = x_1(p_1, ... 0 The Euler Lagrange Equation in words in the context of physical capital accumulation states: Any possible accumulation that may occur at the optimum is brought back to a steady state in the next instant due to the law of motion. This equation communicates the physical properties of our optimum meaning that once we are there no possible improvement from ... 6 The only utility function that comes to mind is the Stone-Geary utility function. For 2 goods, x and y, this takes the form:$$ u(x,y) = (x - a)^\alpha (y- b)^{1- \alpha}. $$This is a Cobb-Douglas type of utility function where a and b are subsistence levels, i.e. you need to consume at least a from x and b from y to survive. It is the ... 5$$y'\frac{x}{y}= -\frac{f_1'(x,y)}{f_2'(x,y)}\frac{x}{y} = - \frac{y^2\exp(x+1/y)}{2y\exp(x+1/y)+y^2\exp(x+1/y)(-y^{-2})}\,\frac{x}{y}=\\=\frac{y^2}{1-2y}\,\frac{x}{y}=\frac{xy}{1-2y}.$$5 This does not seem to have anything to do with calculus. The idea is that the income not consumed Y_d - C is saved (usually denoted by S). This saving is then lent out to companies (via banks) who invest it (usually denoted by I), and the accumulated capital is used in production. I am guessing this is denoted by A? And the change of A in time is ... 4 1. The first question is based on a misreading of the text. First of all it is quite correct that under the model assumptions stated:$$(A) \ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{H(y)^2} y'(d),$$however there is no problem because the book does not state that$$(B)\ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{y'(d)}$$the book instead states that the second ... 2 Although there already is an accepted answer, there is another way to see the global optimality - or rather the same way with a different formulation. By construction,$$\frac{\partial \pi}{\partial b}(b,x) = - G((\beta)^{-1}(b)) + (x-b) \frac{G'((\beta)^{-1}(b))}{(\beta)'((\beta)^{-1}(b))}\Bigg{|}_{b=\beta(x)}= 0,$$where \frac{\partial \pi}{\partial b}(b,... 4 In general the demand for a certain good (say from a consumer) can be written as a function of the prices of all available goods and the total amount of money that the consumer has available. Take the setting of two goods, q_1 and q_2 with prices p_1 and p_2 and total income y. Then the demands can be written as:$$ q_1 = d_1(p_1, p_2, y)\\ q_2 = ...

6

You cannot completely ignore the RHS. Starting with $$\frac{U'(c_{t+1})}{U'(c_{t})}=RHS,$$ replace $t+1$ by $t+\Delta t$ to get $$\frac{U'(c(t+\Delta t))}{U'(c(t))}=RHS_{\Delta t},$$ where $RHS_{\Delta t}$ is the modified version of $RHS$ which contains terms depending on $\Delta t$, e.g. the modified discount factor. Expanding around $c(t)$ (and neglecting ...

6

One way to see (intuitively) the connection between the left hand sides is to write the discrete case as: $$\frac{u'(c(t + \tau))}{u'(c(t))},$$ for $\tau = 1$. Now if we generalise this to a setting where $\tau$ is now a variable in $\mathbb{R}$, this becomes a function of $\tau$. Taking the derivative with respect to $\tau$ and evaluating at $\tau = 0$, ...

4

Dif-in-dif (DiD) strategy relies on the identifying assumption of parallel trend. This essentially means that in the absence of the treatment, the control group and the supposedly treatment group would have evolved similarly (ideally both in the pre-treatment and post-treatment period). The information you provided did not mention anything specific to this ...

0

Total differentiation means you are differentiating all variables in the expression. So if we start with $$y = C\{[y + B - T(y + B)]; [M + \frac{B}{r}]\} + I(r) + G$$ we get: $$d y = C_y^{'} dy + C_y^{'} dB - C_y^{'} dTdy - C_y^{'} dTdB + C_A^{'} dM + C_A^{'} \left( \frac{dBr-Bdr}{r^2} \right) + I'dr + dG$$ Here you are using just basic calculus such as ...

5

$$G(z) (z-x) = \int_x^z G(z) dy$$ and since $G$ is increasing on $[x,z]$, the right hand side is larger than $\int_x^z G(y) dy$.

1

This is probably an old question. However there is a book on PDE's and game theory. Game Theory and Partial Differential Equations, Pablo Blanc and Julio Daniel Rossi. If you found other books on this matter, I would like to know as well.

0

From the buyer's point of view, the "best" supplier is the one who offers them the highest utility. Using the utility function for scoring suppliers seems quite natural then. (In this paper the utility function is assumed to be quasilinear in money, which is just for simplicity.)

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