### Previous Year Paper Solution | Indian Economic Service Exam 2021 | General Economics - I

#### Q. 1(a) - The demand and supply functions are $${P_d} = {\left( {6 - x} \right)^2}$$ and $${P_s} = 14 + x$$ respectively. Find the consumer surplus under pure competitive market.

For solution, See Q. No. 15.29 and 15.30, Chapter - 15, Shaum's Outline Introduction to Mathematical Economics by Edward Dowling, 3rd Edition

#### Q. 1(b) - Distinguish between Economies and Diseconomies of scope. How can the degree of Economies of scope be determined?

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#### Q. 1(c) - How is the inter-temporal pricing a form of price discrimination? Give example.

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#### Q. 1(d) - For a monopsonist, what is the relationship between the supply of an input and the marginal expenditure on it?

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#### Q. 1(e) - Explain divergence between private and social costs and mislocation of resources in a perfectly competitive system.

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#### Q. 1(f) - Describe the methods used in isolating secular trend in a time series.

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#### Q. 1(g) - Distinguish between pure strategies and mixed strategies of a game.

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#### Q. 2(a) - Derive Slutsky equation and interpret it.

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#### Q. 2(b) - Given the utility fuction as $12y = 36 - {x^2}$ and budget line as $M = 12x + 24y$ Determine the utility maximizing basket of the two goods.

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#### Q. 3(a) - Definde cost-output elasticity. Show how it can be used to explain existence or absence of economies of scale in production. Verify your answer on the following: (i) AC = 20 and MC = 10 (ii) AC = MC = 15 (iii) AC = 20 and MC = 30

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#### Q. 3(b) - Given total cost (TC) $$= a + bQ + c{Q^2}$$ Show that $$MC = AC = b + 2\sqrt {(ac)} \,at\,Q = \sqrt {\left( {\frac{a}{c}} \right)}$$ where AC is minimum.

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#### Q. 4(a) - What do the Cournot and Bertrand models have in common? What are the differences between these two models?

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#### Q. 4(b) - Why is it possible for a monopolist to earn supernormal profit in the long-run?

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#### Q. 5(a) - State and explain the modern theory of rent. Show how it can be applied to other factors of production

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#### Q. 5(b) - Explain in terms of the marginal productivity theory how a 'monopolist-monopsonist' firm exploits the society.

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#### Q. 6(a) - Distinguish between Egalitarian society, Utilitarian society Market-oriented society and Rawlsian society.

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#### Q. 6(b) - Using Bergson's welfare contours and grand utility possibility frontier, determine the optimal point of social welfare.

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#### Q. 7(a) - Consider two variable linear regression model: $Y = \alpha + \beta x + u$ The following results are given below: $$\sum {{X_i}} = 228,\,\sum {{Y_i}} = 3121,\,{\sum {{X_i}Y} _i} = 38297,\,\,\sum {X_i^2} = 3204$$ and $${\sum {{x_i}y} _i} = 3347 \cdot 60,\,\,\sum {x_i^2} = 604 \cdot 80$$ and $$\,\,\sum {y_i^2} = 19837$$ and n = 20 Using this data, estimate $$\alpha$$ and $$\beta$$ and the variances of your estimates.

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#### Q. 8(a) - Given the technology matrix $A = \left[ {\begin{array}{*{20}{c}}{0 \cdot 1}&{0 \cdot 3}&{0 \cdot 1}\\0&{0 \cdot 2}&{0 \cdot 2}\\0&0&{0 \cdot 3}\end{array}} \right]$ and final demands are $${F_1}$$, $${F_2}$$ and $${F_3}$$. Find the output levels if $${F_1} = 20,\,{F_2} = 0$$ and $${F_3} = 100$$.

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#### Q. 9(a) - Given the production function as:$Q = A{L^\alpha }{K^\beta };\,\alpha > 0,\,\beta > 0,\,A > 0$ Find the shape of isoquant from the above function.

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#### Q. 9(b) - Defind Elasticity of Substitution of factors. What will be the shape of the isoquant when elasticity of substitution is zero and infinity?

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#### Q. 9(c) - Write down the Constant Elasticity of Substitution (CES) production function and show that Cobb-Douglas (CD) production function is a special case of CES function

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#### Q. 10 - Given the production and cost functions as: $Q = 500{L^{\frac{1}{4}}}{K^{\frac{3}{4}}}$ $C = wL + rK$ (a) Derive the demand curve for labour and capital with a view to maximizing the output when the cost is limited to ₹10,000. Would your answer change if the objective shifts to cost minimization with a desired level of output? Give reasons in support of your answer. (b) Determine the equilibrium levels of employment of the factors in each case given: w = 10 and r = 75

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#### Q. 11(a) - Discuss the notion that the 'bargaining solution' to environmental problems results in the same outcome whether the polluter compensates the sufferers or the sufferers pay the polluter to reduce their levels of emissions.

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#### Q. 11(b) - Why is there a social cost to monopsony power? If the gains to buyer from monopsony power could be redistributed to sellers, would the social cost of monopsony power be eliminated? Explain.

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#### Q. 12 - A local business firm is planning to advertise a special sale on radio and television. Its weekly advertising budget is ₹ 16,000. A radio commercial costs ₹ 800 per 30 - second slot while a television commercial costs ₹ 4,000 per 30 - second slot. Radio slots cannot be bought less than 5 in number while TV slots available are at the most 4 per week. Given that a TV slot is 6 times as effective as a radio slot in reaching consumers, how should the firm allocate its advertising budget to attract the largest number of them? How will the optimal solution be affected if the availability of the television slots is no longer constrained? (i) Formulate LPP model. (ii) Solve the above using graphical method.

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#### Q. 13. a(i) - Explain the concept of direct regression and reverse regression in presence of two variables X and Y. (ii) - Suppose a two variable linear regresssion model without intercept term. Estimate the slope parameter of such a model and show that it is an unbiased estimator. (iii) - Find the value of $${r^2}$$ when the intercept term is absent in the two variable linear regression model.

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