Basic Mathematics for Economic Analysis — DU B.A (Prog.) Economics as Major Previous Year Question Papers

1. Answer the following questions : (9+9) D= [8 17]. Find a matrix X that satisfies (b) Suppose A be the set of rational numbers less than 6; and B be the set of real numbers greater than 3. Universal set is a set of real numbers. (i) Complement of Sets A and B Answer the following questions : (9+9) (a) Examine the convergence of the following sequences with the general term: (b) Let the demand and supply functions of twr commodities 1 and 2 are given below : Write down the equilibrium conditions for two the commodities and solve for Q,, Q,, P,, P2, using Cramer's Rule. 3. Answer the following questions : (9+9) (a) Consider a market for tomatoes, where the supply curve is a straight line, while the demand inction is given by: Q * P = 10. The supply function of this market is such that when the price of tomatoes is Rs 150, the quantity supplied is 10 Kg. However, when the price of tomatoes is Rs 50, the quantity supplied of tomatoes is 2 Kg. Given this information, answer the following, questions: (i) Find the supply fulfction for tomatoes in this market expressed in terms of P and O where P is the price of tomatoes, and Q is the quantity of tomatoes. (ii) Find the equilibrium price and equilibrium quantity of tomatoes traded in the market. (iii) Suppose that due to a bumper harvest, the supply of tomatoes increases in such a manner that it completely changes the f supply function. The new supply curve for. tomatoes is given as: O' = P + 3. Find the new equilibrium price and quantity of tomatoes now traded in the market. Compare the new equilibrium price and quantity against the original equilibrium price and quantity. (b) Write down the given system of equations in matrix notation and then find solutions using the inverse of the coefficient matrix x, + 2xz + x, =4 4. Answer the following questions : (9+ (b) Determine the rank of matrix A, for all values Of p. For what values of p will the matrix be singular? Answer the following questions: (9+9) (a) Given the total cost function C = Q3 - 12Q2 + 60Q, find the marginal and average cost functions. Find the derivative of the average cost function and show the relationship between the AC and (b) Consider a function defined on all real numbers, given by y = f(x) = |x + 4| - 3. Find the values of x at which the following function is continuous and differentiable. 6. Answer the following questions: (a) Given y = (4x12 - 10x2)-3 • use the chain rule lo find dy/dx. Rewrite the function as y = 1/(4x!' - 10x2), find dy/dx by the quotient rule. Are the results identical? (b) A loan valued at 40,000 INR today is to be repaid in equal annual amounts over 10 years, first repayment starting one year from now. The interest rate is 12%. What are the annual amounts? (c) Consider two matrices A and B given below : (i) For what values of x, does the matrix A has an inverse? (i) For what values of y, does matrix B has an inverse? (ii) For what values of x, does the transpose of matrix A has an inverse?