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This particular Assignment references the syllabus chosen for the subject of Economics, for the July 2023 - January 2024 session. The code for the assignment is MEC-203 and it is often used by students who are enrolled in the MAEC (New) Degree.
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Section A
1. a) Explain the necessary and sufficient conditions in case of unconstrained optimisation.
b) Consider a consumer who buys two goods, x and y with utility function u(x, y) = 2√x + y. The consumer's income is 20 and price of y is 4. Compute the optimal consumption bundle when the price of x is equal to 1 using constrained optimisation.
2. With respect to the applications of dynamic optimisation, explain the optimal rate of extraction of exhaustible resources by monopoly.
Section B
3. What is a discontinuous function? Discuss the two types of discontinuous functions along with their diagrams.
4. Explain the concept of a stationary point and inflexion point. Is a stationary point always a point of inflexion? Why or why not?
5. What do you understand by the term ‘joint distribution’ and ‘marginal distribution’? Discuss with the help of an example.
6.What is a sample? Explain with the help of an example. Discuss any two types of sampling techniques.
7) Write short notes on the following:
(i) One-tailed and two-tailed tests
(ii) One to one and onto functions
(iii) Hyperbola
(iv) Local minima
भाग (क)
1. (अ) अनिबाधित इष्टतमीकरण की स्थिति में अनिवार्य और यथेष्ठ स्थितियों की व्याख्या कीजिये ।
(ब) एक ऐसे उपभोक्ता पर विचार कीजिए जो उपयोगिता फलन u (x, y) = 2√x + y के साथ दो वस्तुएँ, x और y खरीदता है । उपभोक्ता की आय 20 है और y की कीमत 4 है। निबाधित इष्टतमीकरण का उपयोग करके, इष्टतम उपभोग बंडल की गणना कीजिये जबकि x की कीमत 1 के बराबर हो ।
2. गतिकी इष्टतमीकरण के अनुप्रयोगों के संबंध में, एकाधिकार द्वारा क्षयशील ( समाप्य) संसाधनों के निष्कर्षण की इष्टतम दर की व्याख्या कीजिए।
भाग (ख)
3. एक असतत फलन क्या है? दो प्रकार के असतत फलनों की उनके रेखाचित्रों के साथ चर्चा कीजिए।
4. एक स्तब्ध (स्थिर) बिंदु और नति परिवर्तन बिंदु की अवधारणा को समझाइए | क्या एक स्तब्ध (स्थिर) बिंदु हमेशा एक नति परिवर्तन बिंदु होता है? क्यों या क्यों नहीं?
5. 'संयुक्त वितरण' और 'सीमांत वितरण' शब्दों से आप क्या समझते हैं? एक उदाहरण की सहायता से चर्चा कीजिए।
6. एक न्यादर्श (प्रतिदर्श) क्या है? एक उदाहरण की सहायता से समझाइए । किन्हीं दो प्रकार की न्यादर्शन (प्रतिचयन) तकनीकों की चर्चा कीजिए।
7. निम्नलिखित पर संक्षिप्त टिप्पणी लिखिए:
i) एक पुच्छ और दो पुच्छ परीक्षण
ii) एकैकी और अनकैकी फलन
iii) अतिपरवलय
iv) स्थानिक अल्पिष्ठिक
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