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Centre for Studies in Diplomacy, International Law and Economics

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(note  please that the expressions of the type p(n) means `p to the power of n', but f(x) stands for a function of x.

                      ECONOMICS (INTERNATIONAL)

                  Time Allowed: 3 Hours Maximum Marks: 100

                                 PART --- 1

   1.Suppose preferences are lexicographic. Then the indifference curves

        a.are kinked 
        b.do not exist 
        c.are straight lines 
        d.are convex to the origin

   1.Let the budget constraint of a consumer be X + Y = 100 and let his utility function be 

U= X + 2Y. Then the consumption of good X is


   1.If the income consumption curve for an individual spending all his income on two goods does
     not slope upwards, then

        a.the individual is irrational 
        b.one of the goods is necessarily a Giffen good 
        c.one of the goods is necessarily an inferior good 
        d.both goods must necessarily be Giffen goods 
        e.both goods must necessarily be inferior goods

   1.A point outside the IS curve but below the LM curve

        a.violates Walras’ law 
        b.indicates excess demand for money and excess supply of goods 
        c.indicates excess supply of money and excess demand for goods 
        d.indicates excess demand for goods as well as bonds 
        e.represents a major monetary crisis

   1.For a Leontief production function the output expansion paths for two different sets of input

        a.intersect once 
        b.are parallel 
        c.are identical 
        d.never intersect 
        e.intersect twice

   1.If the currency deposit ratio and the reserve ratio are respectively 9% and 5%, then the
     money multiplier is approximately

        e.none of the above

   1.The periods of the Third and Fourth Five Year Plans are

        a.1961-62 to 1965-66 and 1969-70 to 1973-74 
        b.1956-57 to 1960-61 and 1961-62 to 1965-66 
        c.1969-70 to 1973-74 and 1974-75 to 1978-79 
        d.1961-62 to 1965-66 and 1966-67 to 1970-71 
        e.not clearly reported in the plan documents

   1.One of the two equal sides of a right-angled triangle whose area is ½ is drawn horizontally
     and divided into (n+1) equal segments. Leaving the first segment, a rectangle is drawn on
     each segment with height equal to the vertical distance from its left-hand end to the
     hypotenuse. The sum of the areas of the rectangles is

        b.n /(n+1) 
        d.½ as n tends to infinity
        e.none of the above

   9.The total cost is given by 5000 + 1000q – 500q(2) + 2/3q(3), where q is the quantity of output.
     If MC = AVC, then 

        a.q = 0 
        b.q = 5000 
        c.q = MC 
        d.q = AVC 
        e.q = 375

   9.If all the resources of an economy are fully employed, then it can produce 1000 units of a
     good. There are only two persons in the economy and the state of the economy is defined as
     a particular way of distributing the good. A state which is not Pareto optimal is

        a.(1000, 0) 
        b.(0, 1000) 
        c.(500, 500) 
        d.(450, 550) 
        e.(450, 450)

                                      PART --- 2

   9.Let the cost function of a firm under perfect competition be C= 0 if q = 0 and C = 1 + 2q(2)
     if q > 0. What is the firm’s supply curve? (one page gap)

12. Determine whether equilibrium solution exists for the following markets:

        a.D = 12 – 3P; S = 2P – 10 
        b.D = 16 – 2P; S = 20 – 2P 
        c.D = 50 – 4P; S = 10 + 10P – P2 

          (one page gap)

          13. Let the consumption expenditure (C) and net investment (I), both functions of
          NNP (Y), be

                    C = 200 + 0.8Y

                    I = 0.1Y – 100

Find NNP in equilibrium. Is this an example of " Paradox of Thrift"? ( one page gap)

  14.If the capital gains on bond holdings are uncertain and the investors maximize utility that
     depends on expected yield and risk, will the relationship between the demand for money and
     the rate of interest be an inverse one? Give reasons. (one page gap)

  15.An economy’s aggregate supply curve is given by Y = 2P, where y is real GNP and P the
     price level. Derive the aggregate demand curve from the quantity theory of money, assuming
     that the money supply is 50 and the velocity of circulation is unity and find the aggregate
     output and the price level in equilibrium. Is the economy in full employment? If not, what
     policy instrument do you see in this model that can increase income and employment? (one
     page gap) 

  16.(a) Maximise x + y subject to 

                    1>_  x + 2y, and

                    1 >_ 2x + y

        a.Find the expected value of a game in which the pay-off is 2n, if head appears at the
          nth toss of an unbiased coin, n=1,2, …,10, and the game stops as soon as head
          appears. (one page gap)

  17.A consumer is observed to purchase x = 20, y = 10 at prices Px =2 and Py = 6. She is

     also observed to purchase x = 18 and y = 4 at prices Px = 3 and Py = 5. Is her behaviour
     consistent with the revealed preference axiom? Give reasons. (one page gap)

  18.(a) A monopolist's demand function is Q = Ap-a, A>0, a>0 and the total cost 

     function is cQ, C>0. For what values of a does there exist a positive profit maximising level
     of output?

     (b) A consumer's utility function is BC(a)L(-b) , a ,b  ,>0, where C is the consumption and L the     labour supply. If Y0 is the consumer's non-wage income, show that the Labour supply curve      is downward sloping if Y0>0. (one page gap)

  19.(a). A man purchases a lottery ticket in which he may win the first prize of Rs. 10,000/- with
     probability 0.001 or the second prize of Rs. 4000/- with probability 0.002. What is his
     mathematical expectation?

     (b). Find the inverse of the following matrix(one page gap)
              a   0  0   0
              0   b  0   0 
               0  0  c   0
               0  0  0  d

  17.Consider a duopoly with identical costs given by C(Qi) = a Qi, a >0. The demand function
     is given by P = A/(Q1 + Q2). What is the Cournot equilibrium ?(one page gap)

                                     Part - III

     21. The market demand is q = 12 - p and the cost function is q(2)/2 (p is price and q,

        a.What would be the equilibrium price and quantity if the firm behaved as a competitive

        b.What would be the equilibrium price and quantity if the firm behaved as a monopolist?

        c.How much money would the firm require if it were to forego the monopoly profit and
          behave competitively?

        d.How much would the consumers be willing to pay if the firm would agree to behave
          as a competitive firm?(one page gap)

     22.A labourer has property income of Rs.20/- per day and works 8 hours a day at Rs.2/-
     per hour. He is indifferent between this situation and another situation in which he sells the
     property to get training in computer science and earns Rs.8/- per hour. In the second
     situation will he work for 8 hours a day or more ? Justify your answer. (one page space)

     23. Write notes on any two of the following. Limit your answer within 200 words:

   a.Uruguay Round of multilateral negotiations

   b.Recent changes in the industrial policy in India

   c.The relevance of the Keynesian model for the Indian economy during the years of the great

   d.Ability-to-pay versus benefit principle. (one page space)




Time Allowed: 3 Hours  Maximum Marks: 100
Questions 1-10 in Part I are multiple choice questions of two marks each. All questions are to be attempted.
Questions 11-20 in Part 2 carry 4 marks each. All questions are to be attempted.
Questions 21 and 22 carry 10 marks each .
Question 23 carries 20 marks 

PART --- 1
(note that in this document m(n) explicitily means m raised to the power of n, but ordinarily f(x) merely implies f is a function of x)

1. Goods X and Y are perfect substitutes. Then the consumer’s indifference curves for these goods are
a. downward sloping straight lines
b. upward sloping straight lines
c. downward sloping but convex to the origin
d. downward sloping but concave to the origin

2. If a firm has a CRS production function and if a firm is paid its value marginal product (VMP), then the profit of the firm is
a. zero
b. strictly positive
c. strictly negative
d. cannot say anything definite

3. Assume that the average variable cost (AVC) curve of a firm is U-shaped. Then at the output level at which the AVC is at its minimum
a. AVC = marginal cost (MC)
b. AVC > MC
c. AVC < MC

4. The first oil shock occurred in the year
a. 1967
b. 1973
c. 1980
d. 1985

5. Suppose money supply increases. Then from the IS-LM diagram
a. the rate of interest (r) increases, the income level (Y) increases
b. r increases, Y decreases
c. r decreases, Y increases
d. r decreases, Y decreases

6. The IS-LM model assumes
a. less than full employment
b. interest rate rigidity
c. wage rate flexibility
d. none of the above

7. Consider the following arguments:
i. a(2) = a(2), where a is some strictly positive number
ii. or, (a - a) (a + a) = 0
iii. or, 2a = 0
iv. or, 2 = 0
a. Step (ii) is wrong
b. Step (iii) is wrong
c. Step (iv) is wrong
d. None of the above
Note: In the question paper, the expression m(n) means:
m raised to the power n 

8. Suppose that there are two goods and both yield strictly positive utility to the consumer. Then the indifference curves are
a. strictly downward sloping
b. strictly upward sloping
c. horizontal
d. vertical

9. Suppose that the production function is linearly homogeneous. Then the output expansion paths are
a. straight lines through the origin
b. L-shaped
c. negatively sloped
d. none of the above

10. A monopolist faces an upward shift in his marginal cost curve. As a result
a. price (p) increases, and output (q) decreases
b. p increases, and q increases
c. p decreases, and q increases
d. p decreases, and q decreases


11. Suppose that the utility function of a consumer is (x – 1)(2) + (y – 1)(2). Plot the demand curve for prices lying between ½ and 2, when his income is 1. (one page gap)

12. Argue that profit maximization implies cost minimization. (one page gap)

13. Let the budget constraint of a consumer be X + Y = 100. Suppose his utility function is given by XY. Argue that he consumes the same amount as a consumer with the utility function 10X(2)Y(2) + 19. (one page gap)

14. Show that in the long run industry equilibrium the marginal firm will produce an output greater than that, which minimizes its average variable cost. (one page gap)

15. Let the consumption be C = 400 + 0.6Y, and let the investment function be I = 100 + 0.2Y.Solve for Y. How would you interpret the model in terms of the IS-LM framework? (one page gap)

16. Discuss the role of expectations in Keynes’ theory of liquidity preference. What would happen to the liquidity preference curve if all individuals had identical expectations? (one page gap)

17. Explain how an increase in the volume of high-powered money leads to an increase in the money supply. (one page gap)

18. In a general equilibrium framework with n markets, why is it enough to look at (n – 1) markets only? (one page gap)

19. If there is a multi-plant monopolist with constant marginal costs and a strictly positive fixed cost for each of the plants, then how many of the plants should he optimally use if the cost function for each plant is the same? (one page gap)

20. Show that if a monopoly is able to practice perfect price discrimination its output will be higher than if it must adopt a conventional pricing policy. (one page gap)


21. Students can buy a travel pass, which entitles them to a reduction in the price of all rail tickets.
a. Show that the introduction of such a pass scheme can never reduce the number of rail journeys a student makes.
b. Show that if a student is indifferent between buying the pass or paying the standard fare, he will never spend less and, in general, will spend more on rail travel if he does buy the pass. (two-page gap)

22. Farmers produce corn from land and labour. The labour cost of producing y is y(2). There are 100 firms, which behave competitively:
a. What is the individual firm’s supply curve of corn?
b. What is the market supply of corn?
c. If the demand function is 200 – 500P, what is the equilibrium price and quantity sold? (two-page gap)

23. Write short notes of any two of the following limiting the total length of your answer to 200 words:
a. Foreign Direct Investment in India
b. Theories of the Consumption Function
c. Optimality of the free market mechanism
d. Causes of depreciation in the foreign exchange value of the rupee since the last quarter of 1995. (two-page gap)




Time Allowed: 3 Hours   Maximum Marks: 100

1. a. A, B, C, D, E are five matrices of n x n dimension. Answer the following and 
  justify your answer (you may use illustrations to justify ):
  i. Given AB = 0, does it imply that either or both of the matrices must be 
   null matrix?
ii. Given CD = CE, does it imply that D = E?
b. Find the present value of a perpetuity yielding a flow of income A per unit of 
 time till infinity, if the continuous rate of discount is r.  3+3+4=10
  (one & half page gap)

2.  Answer any five of the following questions:    5x5=25
 a. Suppose a consumer’s price elasticity of demand for a good X, one of many 
  goods he buys, lies between 0 and 1. Prove that a rise in the price of X will 
  reduce both his demand for X and for at least one of the other goods he buys.
  (half page gap)
b. The price of food rises by 10% and disposable income by 5%. Prove that a person initially spending half his income on food would be better off as a result of these changes. (half page gap)
c. In The case of a production function subject to constant returns to scale show that diminishing marginal productivities imply that more of one input raises the marginal products of the other. (half page gap)
d. In long-run industry equilibrium show that the marginal firm will produce an output greater than that, which minimizes its average variable cost. (half page gap)
e. A monopolist operates subject to a constant elasticity demand curve (with elasticity greater than unity) and constant average costs. If a per unit production tax is levied, show that the price the monopolist charges will rise more than the per unit tax revenue. (half page gap)
f. Show that a consumer’s demand curve for a particular good may be upward sloping for some prices but not for all prices. (half page gap)
g. For f(x) = 1/x, x > 0
Find f(f(x)) and f(df(x)/dx). (half page gap)

3. Answer any three of the following questions in 300 words:  10x3=30
a. What considerations would you have in mind in choosing between an income tax and an excise duty? (one page gap)
b. Discuss the relative advantages and disadvantages of three instruments used by governments to promote investment. Give examples. (one page gap)
c. Empirical investigations reveal that in the short run marginal propensity to consume is less than average propensity to consume but in the long-run they are equal. Discuss any theory of the consumption function that explains this. (one page gap)
d. Would you agree with the view that a market structure dominated by monopolies is essential for innovations and growth in an economy? Argue logically. (one page gap)
e. Should small-scale industries in India be protected from big industries? Give reasons. (one page gap)

4. Write short notes on:       10x3=30
a. Public good. (one page gap)
b. Accelaration principle. (one page gap) 
c. Pareto optimality. (one page gap)

5. Let M = ((x, y): 0 less than or equal to x less than or equal to 1; 0 less than or equal to y less than or equal to 1) and let f(x, y) = cx(2)y.
a. Find the value of c such that f(x, y) is a density function on M.
b. Let A = ((x, y): 1/3 less than or equal to x less than or equal to 2/3; 0 less than or equal to y less than or equal to ½)
and B = ((x, y): ½ less than or equal to x less than or equal to 1; 1/3 less than or equal to y less than or equal to 2/3)
 Evaluate P(A or B), P(A and B) (one page gap)    2+3=5
Note: In the question paper, the expression m(n) means:
m raised to the power of n 

6. An electric current is switched on at random during the day. Then it is switched off at a time selected at random between the time the current is switched on and the end of the day. Let the outcome of this experiment consist of these two times.
a. Describe and sketch the sample space.
b. Find an appropriate density function f(x, y).
c. Sketch the event that the current was on for at least half the day and evaluate its probability.       1+2+2=5
(one page gap)


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