### Previous Year Paper Solution | Indian Economic Service Exam 2010 | General Economics - I

#### Q. No. 1 (a) - Define consumer's surplus. Derive an expression for it using integral calculus.

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#### Q. No. 1 (b) - Why is short-run average cost curve U-shaped? Show that marginal cost curve intersects the average cost curve at latter's minimum point.

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#### Q. No. 1 (c) - Compare long-run equilibrium of the firm under perfect competition with that under monopolistic competition using suitable diagram.

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#### Q. No. 1 (d) - What is a social welfare function? State the underlying assumption in its formulation.

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#### Q. No. 1 (e) - State and explain the assumptions of two variable linear regression model.

Answer to this question is available in Q. No. General Economics - I Previous Year Paper Solution 2013. Assumption of regression and OLS are same because regression is generally done using OLS method.

#### Q. No. 1 (f) What is log-normal distribution? Where is it used in economic analysis?

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#### Q. No. 2 - Derive consumer's expenditure function by minimizing total expenditure; $$y = {p_1}{x_1} + {p_2}{x_2}$$ subject to utility constraint $$\bar u = {q_1}{q_2}$$. (Marks - 15)

Expenditure funtion can be derived if we know either indirect utility function or the compensated demand curve of the two goods. Let us first derive the the compensated demand curve for the two goods.

Here objective is to minimize total expenditure subject to utility constraint. We can write Lagrangian function as follows: $L = {p_1}{q_1} + {p_2}{q_2} + \lambda (\bar u - {q_1}{q_2})$ First order condition for minimization is: $\frac{{\partial L}}{{\partial {q_1}}} = \frac{{\partial L}}{{\partial {q_2}}} = \frac{{\partial L}}{{\partial \lambda }} = 0$ Taking partial derivative of the Lagransian function with respect to q1 and equating to zero, we get: $\frac{{\partial L}}{{\partial {q_1}}} = 0$ ${p_1} - \lambda {q_2} = 0$ $\lambda = \frac{{{p_1}}}{{{q_2}}}$ Similarly, taking partial derivative of the Lagransian function with respect to q2 and equating to zero, we get: $\frac{{\partial L}}{{\partial {q_2}}} = 0$ ${p_2} - \lambda {q_1} = 0$ $\lambda = \frac{{{p_2}}}{{{q_1}}}$ We can equate the values of $$\lambda$$: $\frac{{{p_1}}}{{{q_2}}} = \frac{{{p_2}}}{{{q_1}}}$ Rearranging the equation, we get: ${q_2} = \frac{{{p_1}{q_1}}}{{{p_2}}}$ Sustituting this value of $${q_2}$$ in the utility constraint, we get: $\bar u = {q_1} \times \frac{{{p_1}{q_1}}}{{{p_2}}}$ Rearranging: $\bar u = q_1^2 \times \frac{{{p_1}}}{{{p_2}}}$ ${q_1} = \sqrt {\bar u\frac{{{p_2}}}{{{p_1}}}}$ This is the compensated demand function for Good - 1. Sustituting this value of $${q_1}$$ in the utility constraint, we get: $\bar u = \sqrt {\bar u\frac{{{p_2}}}{{{p_1}}}} \times {q_2}$ Rearranging: ${q_2} = \sqrt {\bar u\frac{{{p_1}}}{{{p_2}}}}$ This is the compensated demand function for Good - 2.
Now, we can find expenditure function by substituting the compensated demand functions in the objective function as follows: $y = {p_1}{q_1} + {p_2}{q_2}$ $y = {p_1} \times \sqrt {\bar u\frac{{{p_2}}}{{{p_1}}}} + {p_2} \times \sqrt {\bar u\frac{{{p_1}}}{{{p_2}}}}$ $y = \sqrt {\bar u{p_1}{p_2}} + \sqrt {\bar u{p_1}{p_2}}$ $y = 2\sqrt {\bar u{p_1}{p_2}}$ This is the expenditure function, we want to find. It can also be written us: $y = 2{{\bar u}^{\frac{1}{2}}}p_1^{\frac{1}{2}}p_2^{\frac{1}{2}}$

Solution video:

#### Q. No. 3 - Draw consumer's indifference curve from revealed Preference Theory.

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#### Q. No. 4 - Separate income effect from substitution effect of a price change for a Giffen type good. Use suitable diagram.

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#### Q. No. 5 - What is elasticity of factor substitution? Give various forms of production function based on this concept.

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#### Q. No. 6 - "Asymmetric or incomplete information leads to market failure." Examine lemons' problem in the above context with the help of pricing of used cars.

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#### Q. No. 7 - What is Hicks-Kaldor criterion of compensation? What are its weaknesses? Give Scitovsky's suggestion for improvement.

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#### Q. No. 8 - Distinguish between positive and negative externalities and explain with examples. Why does government provide some goods which are not public goods?

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#### Q. No. 9 - What are type I and type II errors? Why is probability of type I error fixed in a hypothesis testing problem?

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Solution video:

#### Q. No. 11 - What is Peak-load Pricing? How is it different from third degree price discrimination? Give diagrams to illustrate your answer.

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#### Q. No. 12 - Define production function. The production function for a product is given by Q = 100KL. If price of capital (K) is $120 per day and that of labour (L) is$ 30 per day, what is the minimum cost of producing 400 units of output?

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#### Q. No. 13 -

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1. I substituted the value of $${q_1}$$ into the utility constraint. It already contains the utility constraint so it is like to appear on both size. It is acceptable process in mathematics which we call substitution method.