APPLICATIONS IN STATISTICS-2B — DU B.Sc (hons) Statistics Previous Year Question Papers

Attempt sz.# questions in all. (cE) Discuss briefly the structure of the present offlcial statistics system in India. What pul.pose is served by the collection, compilation and publication of data ? (a) Write short notes on the following : G) NSso and Define price and income e.1asticity of demand. Point out their uses in economic an.alysis. For the demand curve : p = (10 - 2#.) (20 - #2), where # > 0,, p > 0, # is quantity demanded and p is the price. Find the price elasticity of demand at # = 4 and comment on your re suit. ,8 (i) The demand function for a particular commodity is y = .15e-#/3 for 0 < # < 8, where y is the price per unit and # is the number of units delhanded. Determine the price and quantity for which the revenue is maximum. (I.i) The demand curve is # = fry + -2D/2 - 6p2 - 5p4 where y > 0, p > 0, # is quantity demanded, y is incdme and p is. the price. Find slope for demand curve and also check, whether commodity under consideration is normal or inferior. 31/2,31/2 Explain fzuo important method.s commonly used to graduate income distributions, pointing otit their assumptions, merits and demerits. 8 The price elasticity of demand of a commodity is £p where p is the price. Find the coneaponding demand function if it is ]mown that the quantity demanded is 5 units when the price is Rs. 3. 7 a What do you understand by utility function, marginal tltility and rate of change of marginal utility. For the utility function U = #f #2 + 3#| #2, Where #i and #2. are quantities of commodities X[ and X2 respectively, show that the rate of change of marginal utility of commodities Xi w.r.t. X2 is equal to the rate of change of marginal utility of x2 W.I.t. Xi. .7% Derive conditions for the constrained utility maxirisation of utility fimction U = X#, y) subject to budget constraint : pi#i + p2?c:2 = y, where #i, #2 are the quantities consumed and pi, p2 are the prices of the fac7o commodities .Xi and X2 respectively and J is the fixed income. .7% the utility function of.the consumer is given by u = #i#2, Where #i and #2 are c.onsumed quantities of congmodities Xi and X2 reapectively. Find the optimum value of #i and #2 if his income is 91 and product prices are 2 and 5, respectively. 7% Discuss the importance of indifference curve a.nd state its properties. Autilityfunctionisgivena:U=logJg.Findthedemandfuncjion for the commodity X, if fixed income .of the consumer is Rs. 500. Hence, determine the price elasticity of demand. 7% ® What do you mean by production function, average product, marginal product and elasticity of substitution? 7% (a) .Consider a production function as follows : Q = 2L2K? - 3L3K2, where Q is the total output produced, and K is capital and L is labour: (Z) Find average product and marginal product of labour. (Z£) If capital is fixed, find L for which AP will be maximum ? (a.a.i). Does the inaximum of marginal product reach at lower.`level of labour than that of. average product curve\? 2%,21/2,21/2