Problem Book in Relativity and Gravitation最新文献

21. Solutions 21. 解决方案

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-043

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1. Solutions 1. 解决方案

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-023

{"title":"1. Solutions","authors":"","doi":"10.1515/9781400889013-023","DOIUrl":"https://doi.org/10.1515/9781400889013-023","url":null,"abstract":"A very good idea is to start your answer with statements of the relevant definitions — you'll get some marks, and it might steer you clear of pitfalls that can occur when you're not quite clear in your own mind as you consider your answer. 1. F. Define price elasticity of demand; elastic and inelastic demand. If the crop shrinks, then the supply curve shifts left. Price rises, moving up the downwards-sloping industry demand curve. Inelastic demand means that rising price leads to rising revenue, not falling. (Figure 1.) 2. T. Define price-taking (horizontal demand at the going price) and profit-maximising (y * such that MC(y*) = MR(y*) = P(y*), when a price taker). As price rises, will y *, the optimal output also rise? Yes, if MC(y*) rises. And it will, if π is being maximised, not minimised. Indeed, rising MC is necessary for π-maximisation, as shown in all figures in the lectures. (See also the TR and TC curves against output.) (Figures 2a and 2b.) 3. F. Define market power (a downwards-sloping demand curve, so that a monopolist can price above MC to maximise π : the markup , and so does not set P(y*) = MC(y*)), and the supply curve (the maximum amount at any price that a π-maximising firm will offer for sale; or the minimum price at which a π-maximising firm will supply a given amount of output at). The firm chooses y * so that MR(y*) = MC(y*) and sets P > MC(y*), from the demand curve. A firm exercising market power does not have a supply curve, since it is not a price-taker. (Figure 3.) 4. T. We know that the demand curve is linear, but not the choke price P. We also know that the MR curve has the same price intercept (the choke price P), but twice the slope (−ve), so that the MR curve cuts the quantity axis at y = 5, MR(5) = 0. The π-maximiser chooses y * such that MC(y*) = MR(y*). The minimum MC is zero — it cannot be negative — so the maximum output possible is 5 units (incidentally at the point of unitary elasticity on the linear demand curve). (Figure 4.) 5. T. Define opportunity cost. If the sacrifice you make to enjoy more leisure time is forgoing the income (at least) of working in paid employment — and this is implicit in …","PeriodicalId":104035,"journal":{"name":"Problem Book in Relativity and Gravitation","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114548027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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15. The Schwarzschild Geometry 15. 史瓦西几何

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-016

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4. Solutions 4. 解决方案

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-026

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16. Spherical Symmetry and Relativistic Stellar Structure 16. 球面对称与相对论恒星结构

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-017

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15. Solutions 15. 解决方案

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-037

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8. Differential Geometry: Further Concepts 8. 微分几何:进一步的概念

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-010

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9. Curvature 9. 曲率

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-011

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Index 指数

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-044

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12. Gravitation Generally 12. 万有引力一般

Problem Book in Relativity and Gravitation Pub Date : 2018-12-31 DOI: 10.1515/9781400889013-013

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