Recent Questions - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2023-12-01T09:47:24Z https://economics.stackexchange.com/feeds https://creativecommons.org/licenses/by-sa/4.0/rdf https://economics.stackexchange.com/q/57067 0 Heterogeneity analysis for an RCT afreelunch https://economics.stackexchange.com/users/27294 2023-11-30T16:34:11Z 2023-11-30T16:34:11Z <p>Suppose that you are planning an RCT and will estimate how effects vary with baseline covariates. One simple approach uses interactions. That is, if <span class="math-container">$Y_i$</span> denotes the outcome of interest, <span class="math-container">$T_i$</span> denotes the (let's assume binary) treatment that has been randomised, and <span class="math-container">$X_i$</span> denotes a baseline covariate, one estimates the regression <span class="math-container">\begin{equation} Y_i = \beta_0 + \beta_1 T_i + \beta_2 T_i X_i + u_i \end{equation}</span> I have two questions about this:</p> <ol> <li><p>If <span class="math-container">$X_i$</span> is continuous, should one first convert it to a binary variable (e.g. that equals 1 if <span class="math-container">$X_i$</span> exceeds its median)? The results of this exercise seem a bit easier to interpret since <span class="math-container">$\beta_2$</span> becomes the difference in treatment effects between the <span class="math-container">$X_i = 0$</span> and <span class="math-container">$X_i = 1$</span> groups. However, I don't think this is very standard.</p> </li> <li><p>Should one also include <span class="math-container">$X_i$</span> in the regression (above and beyond the interaction term)? I don't really why this is essential, although it does presumably add power.</p> </li> </ol> https://economics.stackexchange.com/q/57064 1 Definition of semi-elasticity robertspierre https://economics.stackexchange.com/users/6887 2023-11-30T10:28:34Z 2023-11-30T10:43:53Z <p>The &quot;<span class="math-container">$x$</span>-elasticity of <span class="math-container">$y$</span>&quot; is defined as <span class="math-container">$\epsilon = \dfrac{\partial y/y}{\partial x/x}$</span>.</p> <p>The <span class="math-container">$x$</span> goes down, and the <span class="math-container">$y$</span> goes up.</p> <p>But we have two definitions of semi-elasticity:</p> <p><span class="math-container">$\epsilon_1 = \dfrac{\partial y/y}{\partial x}$</span></p> <p>Which is the percentage change of <span class="math-container">$y$</span> in response to a (non percentage) change of x, and:</p> <p><span class="math-container">$\epsilon_2 = \dfrac{\partial y}{\partial x/x}$</span></p> <p>Which is the (non percentage) change in <span class="math-container">$y$</span> in response to a percentage change in <span class="math-container">$x$</span>.</p> <p>How do we distinguish between the two?</p> <p>That is, what are they called?</p> <p>When we say &quot;the <span class="math-container">$x$</span>-semi-elasticity of <span class="math-container">$y$</span>&quot;, what do we refer to?</p> <p><strong>REFERENCES</strong></p> <p><a href="https://www.stata.com/manuals/rmargins.pdf#page=26" rel="nofollow noreferrer">STATA manual for rmargins</a>, page 26.</p> <hr /> <p>Note: The actual definition is on <a href="https://www.stata.com/manuals/rmargins.pdf#page=47" rel="nofollow noreferrer">page 47</a>.</p> https://economics.stackexchange.com/q/57061 0 Walrasian equilibrium sophie https://economics.stackexchange.com/users/45733 2023-11-30T00:05:11Z 2023-11-30T13:05:53Z <p>Explain why z(p)=0 is a general equilibrium</p> https://economics.stackexchange.com/q/57060 1 How can I find a Radner equilibrium? Ludwig Gershwin https://economics.stackexchange.com/users/33150 2023-11-29T20:16:57Z 2023-11-29T22:27:38Z <p>Consider an economy with 2 consumers and 1 good. There are 2 dates, date 0 and date 1. At date 1 there are 3 states of nature. The utility functions for the 2 consumers are the same: <span class="math-container">$$u_i(x_i)=\frac{1}{2}\sqrt{x_{i1}}+\frac{1}{3}\sqrt{x_{i2}}+\frac{1}{6}\sqrt{x_{i3}}$$</span> Consumer 1's endowments are <span class="math-container">$w_1=(2,0,0)$</span> and those for consumer 2 are <span class="math-container">$w_2=(0,2,2)$</span>.</p> <p>Suppose there are 2 assets with return vectors <span class="math-container">$r_1^T=(1,0,0),r_2^T=(0,1,1)$</span>. How can I find a Radner equilibrium?</p> <p>Right now I'm trying to solve for Walrasian equilibrium first. I got <span class="math-container">$x_1^*=(1,1,1)=x_2^*$</span>, and the prices at each state are <span class="math-container">$(3,2,1)$</span>. Then I try to find the arbitrage free asset prices, and got <span class="math-container">$q=(5,4,3)$</span>. However, I'm skeptical as the rank of <span class="math-container">$R$</span> is 2, which is not equal to the number of states, so a Walrasian equilibrium and a Radner equilibrium are not equivalent. How do I proceed?</p> <p>In addition, how do I argue that if <span class="math-container">$r_1^T=(1,1,0),r_2^T=(0,0,1)$</span>, then a Radner equilibrium doesn't exist?</p> https://economics.stackexchange.com/q/57059 1 Total cost and public cost of sports stadiums Hilts https://economics.stackexchange.com/users/45731 2023-11-29T17:40:58Z 2023-11-30T10:50:21Z <p>I'm interested in doing data analysis on the cost of large sports stadiums (in the US). I have an excellent data source in &quot;Financing Professional Sports Facilities&quot; (Robert A. Baade, Victor Matheson) but it only goes up to 2011. The scholarly literature on this is vast, but I'm wondering if anyone's done any comparable tabulating for the period after 2011?</p> https://economics.stackexchange.com/q/57058 1 Credit profile bank dataset for Machine learning Player 777 https://economics.stackexchange.com/users/45730 2023-11-29T17:17:47Z 2023-11-30T10:59:49Z <p>Can you advise please any credit profile Bank free available datasets for Markov chain and machine learning computational experiments? For my student masters thesis. Thank you.</p> https://economics.stackexchange.com/q/57057 0 Aggregate elasticity of demand in a differentiated products market Dale https://economics.stackexchange.com/users/45726 2023-11-29T11:37:43Z 2023-11-29T11:37:43Z <p>Is the notion of aggregate elasticity of demand applicable in a market for slightly differentiated products? Intuitively, it seems like it should. If market output can be expressed in a single number (for example, the number of cars in a market of cars differentiated by color), then if the price of each of the products is increased by the same small percentage, you could calculate an aggregate elasticity. Is this an accepted concept in economics?</p> https://economics.stackexchange.com/q/57053 1 If utility function is convex, what can be said about preference relation? Paul R https://economics.stackexchange.com/users/45426 2023-11-29T06:00:20Z 2023-11-29T09:02:56Z <p>It is known that if a utility function is concave, then it is quasiconcave, and the preference relation is convex.</p> <p>What can be said if a utility function is convex?</p> <p>I've found on the Internet then in this case the function can be both quasiconcave and quasiconvex (how is this possible? linear function?) and is in this case preference relation concave?</p> <p>I've managed to show that the utility function <span class="math-container">$u(x_1,x_2)=\operatorname{max}(x_1,x_2)$</span> is convex. What can be said about the preference relation?</p> https://economics.stackexchange.com/q/57051 1 About infinite strategy sets and $\epsilon$-equilibrium from Game Theory: Analysis of Confilct by Roger Myerson Beerus https://economics.stackexchange.com/users/44386 2023-11-28T23:57:27Z 2023-11-29T08:03:15Z <p>I am studying infinite strategy sets using Myerson's Game Theory: Analysis of Conflict. On Page 143, he defines an <span class="math-container">$\epsilon$</span>-equilibrium as follows:</p> <blockquote> <p><strong>Definition</strong> For any nonnegative number <span class="math-container">$\epsilon$</span>, an <span class="math-container">$\epsilon$</span>-equilibrium of any strategic-form game is a combination of randomized strategies such that no player could expect to gain more than <span class="math-container">$\epsilon$</span> by switching to any of his feasible strategies, instead of following the randomized strategy specified for him. That is, <span class="math-container">$\sigma$</span> is an <span class="math-container">$\epsilon$</span>-equilibrium of <span class="math-container">$\Gamma$</span> if and only if <span class="math-container">\begin{align*} u_i(\sigma_{-i},[c_i]) - u_i(\sigma) \leq \epsilon,\quad \forall i \in N,\quad \forall c_i \in C_i.\tag1 \end{align*}</span></p> </blockquote> <p>Then, he put:</p> <blockquote> <p>when <span class="math-container">$\epsilon=0$</span>, an <span class="math-container">$\epsilon$</span>-equilibrium is just a Nash equilibrium in the usual sense.</p> </blockquote> <p>However, I am a bit confused about this expression (1), because of that &quot;<span class="math-container">$[c_i]$</span>&quot; there. Expression (1) means that no player could expect to gain more than <span class="math-container">$\epsilon$</span> by switching to any of his <em><strong>pure</strong></em> strategies (not <em><strong>feasible</strong></em> strategies, because they might as well be mixed strategies <span class="math-container">$\tau_i$</span>). So I feel that the definition should have been stated as:</p> <blockquote> <p><span class="math-container">$\sigma$</span> is an <span class="math-container">$\epsilon$</span>-equilibrium of <span class="math-container">$\Gamma$</span> if and only if <span class="math-container">\begin{align*} u_i(\sigma_{-i},\tau_i) - u_i(\sigma) \leq \epsilon,\quad \forall i \in N,\quad \forall \tau_i \in \Delta(C_i).\tag2 \end{align*}</span></p> </blockquote> <p>I would like to know if my thought is correct. Is this a mistake of the book, or is the amended definition and expression unnecessary? I would really appreciate it if someone could help me check!</p> https://economics.stackexchange.com/q/57050 1 If utility function is homogenous of order 1, then partial derivatives of demand function are equal Paul R https://economics.stackexchange.com/users/45426 2023-11-28T23:16:31Z 2023-11-29T08:17:04Z <p>Prove that if <span class="math-container">$U(\alpha x)=\alpha U(x)$</span>, then <span class="math-container">$$\frac{\partial x_i(p,w)}{\partial p_j}=\frac{\partial x_j(p,w)}{\partial p_i}$$</span> for any <span class="math-container">$i$</span> and <span class="math-container">$j$</span>.</p> <p>I've proved that <span class="math-container">$x(p,\alpha w)=\alpha x(p,w)$</span>, but I don't know how to handle partial derivatives.</p> https://economics.stackexchange.com/q/57049 0 Second-degree price discrimination exercise Sofia Delacruz https://economics.stackexchange.com/users/45724 2023-11-28T21:47:29Z 2023-11-29T07:17:43Z <p>A monopolist produces output with constant marginal cost equal to 1. There are two of consumers that are potentially in the market for the good. Consumer A has inverse demand function <span class="math-container">$$p_A(x) = 7 − x,$$</span> and consumer B has inverse demand function <span class="math-container">$$p_B(x) = 5 − x.$$</span></p> <p>Suppose the monopolist cannot identify which consumer is which. What is the best pair of purchase options <span class="math-container">$(x_A, R_A)$</span> and <span class="math-container">$(x_B, R_B)$</span> the monopolist should offer? (Hint: You’ll need to show that <span class="math-container">$x_B = 2.$</span>) What is the firm’s profit?</p> <p>My attempt:</p> <p>The question doesn't make clear what <span class="math-container">$R_A, R_B$</span> are. But I guess the question is asking about 2nd degree price discrimination. So type A is high-demand consumer and B is low-demand consumer. <span class="math-container">$MR_B=5-2q_B=1$</span>, then <span class="math-container">$x_B^*=2$</span> and at this point, the price is 3. So the first bundle designed for low-demand consumer is (2 units, whole bundle price is 2x3=6). I still need to design the other bundle for high-demand consumer.</p> <p>If high-demand consumer pretends to be low-demand and buys the above bundle, so he or she buys 2 units and pays $6. His or her WTP is 12. So consumer surplus is 12-6=6. Then how should I do next?</p> https://economics.stackexchange.com/q/57048 0 Marginal and Average costs for constant returns to scale production function being constant Nick https://economics.stackexchange.com/users/45723 2023-11-28T20:24:24Z 2023-11-30T10:21:31Z <p>Suppose that we are dealing with a production function <span class="math-container">$q = f(k,l)$</span>, of inputs capital and labor. If this function exhibits constant returns to scale then I know that both the marginal cost and average cost functions <span class="math-container">$C(q)$</span> are equal and constant for each of the inputs and the total. i.e: <span class="math-container">$$\frac{\partial C(q)}{\partial q} = \frac{C(q)}{q}$$</span>This means that the contingent demand for labor and capital must be linear in <span class="math-container">$q$</span>. Why is this is case mathematically and what is the economic interpretation?</p> https://economics.stackexchange.com/q/57047 0 Engine efficiencies on small scale ( ice engines vs turbines Doctor Pinocchio https://economics.stackexchange.com/users/45719 2023-11-28T00:29:55Z 2023-11-28T02:35:08Z <p>A formula one engine is around 51% efficient (and if it weren't for the regulation and rules it might have been close to 55 to 60% efficient read somewhere in Google) that the extreme side but there are engines which are more than 50% efficient eg.&quot;achates power opposed postion engine&quot;, &quot;Toyota free piston engine&quot; (net efficiency thermal to electric) on the other hand a state of the art coal powerplant are 47.7% efficient while producing more emissions and is not as flexible with fluctuating demands (it drops efficiency if done so).</p> <p>Here comes the economic aspect, the 47.7% efficient coal power plant is located in German (rdk8) costs 4,500,000 usd per megawatt and sells it's electricity for$35-39 MWh (roughly)</p> <p>If replaced with the above mentioned ice engines (not f1 engine), then we can see that it would cost 5,500,000 usd per megawatt but can sell its electricity for more than double the price to $88-95 MWh (assuming it from natural gas plants)</p> <p>Even though the fuel costs are higher compared to coal you should be able to generate more profit (based on some questionable napkin math), so why not?</p> https://economics.stackexchange.com/q/57044 0 Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent pacmanscuriousbloob https://economics.stackexchange.com/users/45710 2023-11-27T13:07:10Z 2023-11-27T17:31:07Z <p>I have been trying to use the contradiction method to prove this, but it does not seem to be working.</p> <p>Suppose <span class="math-container">$x^*$</span> is optimal in both EMP and UMP. Then <span class="math-container">$u(x^*) \geq u(x')$</span> for all <span class="math-container">$x'$</span> in <span class="math-container">$B_pw$</span>.</p> <p>And <span class="math-container">$p.x^*$</span> &lt; <span class="math-container">$p.x'$</span> <span class="math-container">$\leq w$</span></p> <p>Also <span class="math-container">$x^*$</span> is optimal in UMP. So <span class="math-container">$u(x^*)$</span> &gt; <span class="math-container">$u(x')$</span> for all <span class="math-container">$x'$</span>.</p> <p>I can't find a way to reach a contradiction here. Is it that the demand correspondence lies on the budget plane so there is no way LNS can hold because it would lie outside Bp,w?</p> <p>This is basically MWG proposition 3.E.1 without the LNS assumption.</p> <p><em>Show that if <span class="math-container">$x^*$</span> is optimal in the utility maximization problem when <span class="math-container">$w &gt; 0$</span>, then <span class="math-container">$x^*$</span> is optimal in the expenditure minimization problem when the constraint is to attain a utility level <span class="math-container">$u(x^*)</span>.</em></p> https://economics.stackexchange.com/q/56830 1 Could a global tax agreement improve the Gini coefficient for income in all countries? user43089 https://economics.stackexchange.com/users/0 2023-10-30T23:14:56Z 2023-11-30T06:19:05Z <p>Does this line of reasoning make sense in terms of economic agents, even if implementation is highly unlikely?</p> <ol> <li><p>The Gini coefficient is an imperfect but reasonable measure of income inequality within a country.</p> </li> <li><p>One reason that governments avoid increasing income tax on high earners is that they will move to another country with lower taxes.</p> </li> <li><p>Therefore, if all countries agreed to a certain level of high-income tax (&quot;we will all tax our highest earners at least 45%&quot;), there would be no incentive to move and all countries could tax their high earners more.</p> </li> <li><p>Governments could use the taxes to pay for labor, or basic income, which should improve the Gini coefficient for income in their country.</p> </li> </ol> <p><strong>Footnotes</strong></p> <ul> <li><p><strike>I've never quite understood claim 2, because firstly you are taxed on income not wealth, and secondly I assume you can't simply transfer huge amounts of money between countries.</strike> I've focused on income.</p> </li> <li><p>Although claim 3 seems unlikely, in 2021 the G7 reached an agreement on taxing corporations:</p> </li> </ul> <blockquote> <p>The United States, Britain and other large, rich nations reached a landmark deal on Saturday to squeeze more money out of multinational companies such as Amazon and Google and reduce their incentive to shift profits to low-tax offshore havens.</p> <p><a href="https://www.reuters.com/business/g7-nations-near-historic-deal-taxing-multinationals-2021-06-05/" rel="nofollow noreferrer">https://www.reuters.com/business/g7-nations-near-historic-deal-taxing-multinationals-2021-06-05/</a></p> </blockquote> https://economics.stackexchange.com/q/55766 1 Can someone help me how to perform quarterly chain linking? Johannes https://economics.stackexchange.com/users/44527 2023-07-03T16:10:50Z 2023-12-01T00:03:20Z <p>Assume we have given apples and oranges; If we only consider annual chain-linking, it is pretty simple, e.g. let us have the following values:</p> <div class="s-table-container"> <table class="s-table"> <thead> <tr> <th style="text-align: left;"></th> <th style="text-align: center;">Year 1</th> <th style="text-align: right;">Year 2</th> <th style="text-align: right;">Year 3</th> <th style="text-align: right;">Year 4</th> </tr> </thead> <tbody> <tr> <td style="text-align: left;">Apples</td> <td style="text-align: center;">Amount: 10, Price:3, Total 10*3=30</td> <td style="text-align: right;">Amount: 8, Price:4, Total 8*4=32</td> <td style="text-align: right;">Amount: 7, Price:5, Total 7*5=35</td> <td style="text-align: right;">Amount: 5, Price:10, Total 5*10=50</td> </tr> <tr> <td style="text-align: left;">Oranges</td> <td style="text-align: center;">Amount: 5, Price:4, Total 5*4=20</td> <td style="text-align: right;">Amount: 7, Price:4, Total 7*4=28</td> <td style="text-align: right;">Amount: 7, Price:4, Total 7*4=28</td> <td style="text-align: right;">Amount: 10, Price:3, Total 10*3=30</td> </tr> <tr> <td style="text-align: left;">Total</td> <td style="text-align: center;">30+20=50</td> <td style="text-align: right;">32+28=60</td> <td style="text-align: right;">35+28=63</td> <td style="text-align: right;">50+30=80</td> </tr> </tbody> </table> </div> <p>I now want to get the chain linked volumes with the reference year 1; To do so I first calculate for each year &quot;Current volume * previous year price&quot;</p> <div class="s-table-container"> <table class="s-table"> <thead> <tr> <th style="text-align: left;"></th> <th style="text-align: center;">Year 1</th> <th style="text-align: right;">Year 2</th> <th style="text-align: right;">Year 3</th> <th style="text-align: right;">Year 4</th> </tr> </thead> <tbody> <tr> <td style="text-align: left;">Apples</td> <td style="text-align: center;">Amount: 10</td> <td style="text-align: right;">Amount: 8, Previous Price:3, Total 8*3=24</td> <td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td> <td style="text-align: right;">Amount: 5, Previous Price:5, Total 5*5=25</td> </tr> <tr> <td style="text-align: left;">Oranges</td> <td style="text-align: center;">Amount: 5</td> <td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td> <td style="text-align: right;">Amount: 7, Previous Price:4, Total 7*4=28</td> <td style="text-align: right;">Amount: 10, Previous Price:4, Total 10*4=40</td> </tr> <tr> <td style="text-align: left;">Total</td> <td style="text-align: center;"></td> <td style="text-align: right;">24+28=52</td> <td style="text-align: right;">28+28=56</td> <td style="text-align: right;">25+40=65</td> </tr> </tbody> </table> </div> <p>Now to get the chain-linked volumes with Year 1 as a reference Year I simply use that for the reference year, chain-linked volumes are equal to current prices and for Year 2,3 and 4 I can use that &quot;Current volume * previous year price&quot; / &quot;Previous year's price * previous year's volume&quot; = Chain linked volume of current year/Chain linked volume of previous year (all with same reference year);</p> <p>So e.g. for Year 2, I just take 52/50 * Chain Linked volume year 1 = 52/50*50 = 52; This leads to the following table for the total of oranges+apples</p> <div class="s-table-container"> <table class="s-table"> <thead> <tr> <th style="text-align: left;"></th> <th style="text-align: center;">Year 1</th> <th style="text-align: right;">Year 2</th> <th style="text-align: right;">Year 3</th> <th style="text-align: right;">Year 4</th> </tr> </thead> <tbody> <tr> <td style="text-align: left;">Total</td> <td style="text-align: center;">50</td> <td style="text-align: right;">52/50*50=52</td> <td style="text-align: right;">56/60*52=48.53333</td> <td style="text-align: right;">65/63*48.53333= 50.07</td> </tr> </tbody> </table> </div> <p>Of course, one could do something similar not just for the total but also for oranges and apples itself but this would just give volume*price of the base year (Year 1), so chain-linking would be identical to calculating with prices of a base year;</p> <p>As easy as this is, I am now trying to understand how quarterly chain-linking works; Assume we have again 4 years but with quarters 1,2,3,4 and for each quarter, we have an amount of apples, an amount of oranges, a price per apple and a price per orange;</p> <p>How would I then calculate the quarterly chain-linked volume?</p> https://economics.stackexchange.com/q/54557 0 Trade and Opportunity Cost Shreevani https://economics.stackexchange.com/users/43591 2023-02-26T08:36:27Z 2023-11-29T19:01:45Z <p><a href="https://i.stack.imgur.com/IdqlC.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/IdqlC.jpg" alt="Please help me with this question" /></a></p> <p>This is a question on opportunity cost. I had problem in solving the last part. Please help me out.</p> https://economics.stackexchange.com/q/54269 2 Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space? user10478 https://economics.stackexchange.com/users/41978 2023-01-29T02:55:42Z 2023-11-30T00:08:21Z <p>It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play any of...</p> <ul> <li>Throw rock and blink</li> <li>Throw rock and do not blink</li> <li>Throw paper and blink</li> <li>Throw paper and do not blink</li> <li>Throw scissors and blink</li> <li>Throw scissors and do not blink</li> </ul> <p>Game theory would be pretty useless in the real world if solutions to the &quot;new&quot; game this creates could not be analyzed by partitioning this strategy space into the superstrategies...</p> <ul> <li>Rock strategies</li> <li>Paper strategies</li> <li>Scissors strategies</li> </ul> <p>...and applying the tools used to solve the ordinary version of Rock Paper Scissors to these superstrategies (at least up to some imperceptible negative utility of blinking). Can we, in general, less trivial contexts, port the tools of game theory ordinarily applied to strategies (dominant and dominated strategies, iterative deletion, best responses, Nash Equilibria and other solution concepts, backward induction, etc.) over to these superstrategy partitions of a strategy space?</p> <p><strong>Example #1:</strong> In a trading card game, a player builds a custom deck of cards to battle another player with. Suppose there are <span class="math-container">5000$</span> cards available, and each deck must contain <span class="math-container">$50$</span> unique cards. Then the player has <span class="math-container">$5000 \choose 50$</span> possible pure strategies for building a deck or mixing over. Further suppose we come up with an algorithm which categorizes each strategy as either aggressive (meaning the probability of the resulting deck [or expected deck if mixing] winning a battle is higher in shorter games; it is suited to the role of expending resources ambitiously to seek a fast victory), or passive (meaning the probability of the resulting deck or expected deck winning a battle is higher in longer games; it is suited to the role of waiting for the opponent to expend resources before seeking to win). We <em>could</em> apply any of the usual tools of game theory to strategies, but the strategy space is huge. The approach under consideration in this question is to apply the same tools to the superstrategies...</p> <ul> <li>Build an aggressive deck</li> <li>Build a passive deck</li> </ul> <p>For example, a superstrategy profile might be considered a Nash Equilibrium iff both players with common knowledge of whether the other has chosen an aggressive deck or a passive deck still do not benefit by switching their own deck from aggressive to passive, or vice-versa. They are allowed to benefit by switching to a different strategy within the same superstrategy (i.e., switch from one aggressive deck to a different aggressive deck). Depending on how the finer details are defined, one strategy switch per player may guarantee that no one is better off switching a second time, but if a player is allowed to see that their opponent switched, for example, and that new information incentivizes them to switch again, then no matter how many times players switch while converging to or cycling between strategies, they should not be incentivized to deviate from their superstrategy.</p> <p><strong>Example #2:</strong> Consider a three-player game of Monopoly. I'm not sure if real Monopoly is guaranteed to halt, so assume some arbitrary modifications to the rules to keep things finite, if it matters. Even if finite, the strategy space is huge, but perhaps we think an important factor for predicting outcomes is knowing which players are included in property trades. In real Monopoly, players sometimes collude against the player(s) perceived to be the most skilled at the game by refusing to trade with them. Suppose we design our algorithm to categorize each of Player A's strategies as one of the superstrategies...</p> <ul> <li>Attempt to collude with Player B against Player C</li> <li>Attempt to collude with Player C against Player B</li> <li>Do not attempt to collude against either opponent</li> </ul> <p>Player B and Player C would each have three analogous superstrategies. Maybe here we want to evaluate whether Player A colluding against Player C is dominated by colluding against Player B. I can think of at least two senses in which this might be defined...</p> <ul> <li>Regardless of which strategies Player B and Player C choose, Player A is always better off playing at least one strategy within the collusion against Player B superstrategy than any strategy within the collusion against Player C superstrategy, though knowing the other players' strategies may influence <em>which</em> strategy within the collusion against Player B superstrategy Player A prefers; the invariant is that no strategy within the collusion against Player C superstrategy is ever better</li> </ul> <p>OR</p> <ul> <li>Regardless of which superstrategies Player B and Player C choose, Player A is always better off in expectation playing at least one strategy within the collusion against Player B superstrategy than any strategy within the collusion against Player C superstrategy, though learning the other players' exact strategies may incentivize Player A to switch to a different superstrategy</li> </ul> <p>Do game theoretic tools extend in this way, possibly with slight modification if I've described them incorrectly? If so, then can qualitative game theoretic conclusions about a game change depending on how finely or coarsely the strategy space is partitioned into superstrategies? If not in general, then how far can this idea be pushed beyond the completely trivial examples before it stops producing correct results?</p> https://economics.stackexchange.com/q/53266 1 Finding data on high paying jobs Cayley-Hamilton https://economics.stackexchange.com/users/42613 2022-10-27T05:26:10Z 2023-11-28T22:01:00Z <p>This is a pretty beginner question. My background is in pure mathematics, and I know statistics and R, but no economics.</p> <p>It might be a bit much tagging this as a data request question since I'm trying to get a sense of some of the basics.</p> <p>I'm interested in statistics concerning the highest earning jobs, along with other associated information such as age, gender, and education.</p> <p>Is there somewhere where economists would usually go to access these kinds of figures...</p> <ol> <li>...if they were interested in doing serious statistics</li> <li>...if they were interested in a quick but scholarly search for an unimportant question.</li> </ol> <p>Right now I'm only curious about figures involving high income, but maybe the answer here involves a good source of data overall -I'd benefit from that as well.</p> https://economics.stackexchange.com/q/51948 0 The concept of 'truthfulness' and 'indirect' in mechanism design John Wong https://economics.stackexchange.com/users/41639 2022-07-03T15:21:43Z 2023-11-30T13:04:51Z <p>I'm a beginner in mechanism design. I learned that 'a (direct) mechanism is truthful if an agent truthfully reveals his/her type.' Then, how can we define a truthful indirect mechanism? I'm not sure how to do that because the information revealed in an indirect mechanism can be any message, which is in general different from the underlying type.</p> <p>Thanks!</p> https://economics.stackexchange.com/q/50981 1 Did online learning affect the returns to education? csilvia https://economics.stackexchange.com/users/28068 2022-04-04T17:01:55Z 2023-11-30T14:55:41Z <p>I am interested to know if online learning during the pandemic affected the returns to university education. Anecdotally, education quality suffered from online learning, I wonder if this harmed students' wages.</p> <p>Is there any paper or report that tried to look at this topic empirically?</p> https://economics.stackexchange.com/q/50670 0 How would you measure automation or technological development? Meriç Gür https://economics.stackexchange.com/users/40665 2022-03-07T16:54:15Z 2023-11-28T02:04:50Z <p>Hello dear Economists,</p> <p>I am a Political Science Masters student and now I have this paper due 10 days. It is only a paper so I should not model something too complex and also I obviously lack the economics understanding for it.</p> <p>What I am trying to do is, I want to see whether automation or technological development in general has an effect on governments education policy. This is the big question. Specifically I will use the Varieties of Capitalism approach and want to test the idea whether, lately, Coordinated Market Economies are also teaching more general skills rather than specific skills like Liberal Market Economies. In theory Coordinated Market Economies systems should differ in terms teaching, yet, It is now also often argued automation and technology has an impact on skillsets as well and people with specific skills are more in danger (I am not talking about STEM grads,engineers etc but more like machine operators) as they cant change industries that easy. Again, this paper is not going to be published anyware, it is very basic and I think the professor's expectation is whether we can construct solid arguments and integrate R and analysis to our paper.</p> <p>What I am confused a little is how to measure the technological development/automation side of things. I did a little research myself and there are different approaches like using Total Factor Productivity or I also found robot density for manufacturing sector in 2020 but the data is very limited and also for skills side of the equation there is no data available for 2020. I am using post-secondary non tertiary education to capture the skills part (I am arguing this captures the vocational education so skills thought are specific, I am aware it is problematic as well.)</p> <p>So I wanted to ask if do you have any reccomendations on how to measure the countries automation or tech development level, I would greatly appreciate any criticism or feedback.</p> https://economics.stackexchange.com/q/44299 1 Is the book by Nicholson and Snyder more rigorous when compared to Varian's Intermediate Microeconomics? NSvsV https://economics.stackexchange.com/users/35018 2021-06-03T03:41:01Z 2023-11-30T15:00:00Z <p>I am about to start learning college level Economics and the two books that are commonly used are <em>Intermediate Microeconomics</em> by Hal Varian and <em>Microeconomic Theory: Basic Principles and Extensions</em> by Nicholson and Snyder.</p> <p>I know for a fact that the Varian's book is used by almost everybody as their introduction to the subject. However, a quick glance makes me feel that the latter is more mathematically rigorous an has better problems (and by this, I do not mean the beginning chapter that teaches the mathematical pre-requisites).</p> <p>Is Nicholson &amp; Snyder actually more rigorous? How good will it be for someone who intends to make progress in the subject rather rapidly and explore the mathematics aspects of it in the long run? What am I going to miss and learn more by not doing the book by Varian?</p> https://economics.stackexchange.com/q/32873 1 What would cause the velocity of money (V) to increase / accelerate (or at least stop falling) recovery bubble https://economics.stackexchange.com/users/24964 2019-11-21T07:15:41Z 2023-11-30T23:03:00Z <p>Given that:</p> <p>MV=PY</p> <p>Or</p> <p>P = (M)(V) / Y</p> <p>Where M is the money supply, V velocity of money, P price level and Y real GDP</p> <ol> <li>Considering that the current rate of M2 is increasing at 7% per year over the last 12 months, and real GDP is now forecasted to decelerate from 1.9%/year to maybe as low as .4% by the end of Q4 2019, (according to the Atlanta Fed), am I correct to assume, going forward, that even the slightest sustained increase in (V) would rocket inflation from our current 1.7% per year to something resembling an inflation rate of over 7% in the very near future?</li> </ol> <p>My primary question is this: what event(s) or scenerio(s) can you think of that would cause the velocity of money (V) to start increasing / accelerating again; or at the very least, stop falling like it has over the last 9 years?</p> <p>Would V be expected to increase as a result of a mass exiting of the stock market (frigtened stock market investors liquidating their retirement holdings into cash and then spending it)?</p> <p>For instance, the stock market starts falling and worried baby boomers start cashing out their retirement accounts and then start spending it on things like medical care, prescription drugs, on retirement housing, vacations, RVs, ect?</p> <p>Or maybe baby boomers start dying and their children start taking the inheritance money and spending it all on consumer goods; buying sports cars, electronics, vacations, boats, ect?</p> https://economics.stackexchange.com/q/32850 0 Correlation between nominal bond returns and growth Jr Analyst https://economics.stackexchange.com/users/24952 2019-11-20T17:55:31Z 2023-11-30T11:08:36Z <p>I read the following passage and the bolded section has me confused: </p> <blockquote> <p>In theory, assets earn a low (or negative) risk premium if they tend to perform well when the economy is weak. <strong>When growth and inflation are primarily driven by aggregate demand, nominal bond returns tend to be negatively correlated with growth</strong> and a relatively low term premium is warranted. Conversely, <strong>when growth and inflation are primarily driven by aggregate supply, nominal bond returns tend to be positively correlated with growth</strong>, necessitating a higher term premium.</p> </blockquote> <p>I thought that growth and nominal bond returns were usually negatively correlated. Why would the growth being supply or demand-driven affect this correlation?</p> <p>Thank you for any and all answers!</p> https://economics.stackexchange.com/q/32809 3 How to test if the effect of one regressor entirely comes from other regressors? Alex Wang https://economics.stackexchange.com/users/24926 2019-11-17T20:55:54Z 2023-12-01T06:05:35Z <p>I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know whether the only way parents'education increases my IQ test score is through my own education. How would I test that hypothesis? </p> https://economics.stackexchange.com/q/25710 0 annualized quarterly growth rate calculating user20269 https://economics.stackexchange.com/users/20269 2018-11-23T10:39:28Z 2023-11-27T22:01:50Z <p>I was using R to calculate the annualized quarterly growth rate of real GDP by 400*diff(log(rgdp)).</p> <p>If I perform in this way some of the percentage change is big.</p> <p>However, if I calculate as 100*diff(log(rgdp)) than results seems to be accurate as what shows up on the most of the website.</p> <p>Why is this happening? follow by the growth formula it should be multiplied by 400, not 100.</p> https://economics.stackexchange.com/q/24658 0 Monopsony diagram curves Yang https://economics.stackexchange.com/users/19293 2018-09-24T13:53:01Z 2023-11-28T06:04:10Z <p>Why is the marginal cost curve not the same as the supply curve?</p> <p>My personal explanation is that since the marginal cost curve is cost of producing each new product, the supply curve just represents the break even point of selling a certain number of these products. The seller can sell some at a profit, and some at a loss, and as long as the loss and profit cancel out, he's on the supply curve. Thus the supply of producing x goods is just the average of the marginal cost curve from 0 to x.</p> <p>This explanation seems logical to me, but I have been given an alternative explanation - the supply curve is that of the market, whereas the marginal cost curve is intrinsic to the firm. However, I am unsure as to why the market supply would be related to the marginal cost curve as the average of its integral.</p> https://economics.stackexchange.com/q/21603 0 Does the Marginal Propensity to Import = negative Marginal Propensity to Tax? Fred Wieser https://economics.stackexchange.com/users/15692 2018-04-22T15:15:25Z 2023-11-30T07:01:00Z <p>the multiplier$= \frac{1}{(1-MPC)}$</p> <p>and </p> <p>the multiplier$= \frac{1}{MPW} = \frac{1}{MPS+MPM+MPT}$.</p> <p>Now since$MPC + MPS = 1$it follow that$1-MPC = MPS$,</p> <p>therefore the multiplier =$\frac{1}{(MPS+MPM+MPT)} = \frac{1}{MPS}$</p> <p>and so$MPS = MPS + MPM + MPT$</p> <p>from this, we can see that$MPM = -MPT\$</p> <p>Therefore, Marginal Propensity to Import = negative Marginal Propensity to Tax</p> <p>I am unable to see what the flaw in the logic is or if there is something I am missing. Any explanation or help would be great.</p> https://economics.stackexchange.com/q/9038 5 Growth theory / Initial GDP: positive coefficient sign user6171 https://economics.stackexchange.com/users/6171 2015-11-06T16:09:16Z 2023-11-28T05:06:15Z <p>I estimated growth regressions for several EU countries. In each of them, the sign of "initial GDP"'s coefficient is statistically significant but positive, which contradicts growth theory as well as most of other published papers on this topic. I tried to change the variables, the period, etc. but it remains positive.</p> <p>I can't find any explanation for this result in the literature, which would imply that there is no growth convergence among European countries.</p> <p>Did anybody already face this problem? How did you solve this? I can't find the source of this problem. Personally, I replaced "initial GDP" by "lagged (one period) GDP" but it would be better if I could keep "initial GDP" among the explanatory variables.</p>