Business Mathematics — DU B.Com. (Hons.) Previous Year Question Papers

1. (a) For two industries, input-output relationship (in units) is as follows : Final Demand Gross Output Labour Days Using matrix notations, determine: (i) Gross output required to satisfy the new final demand of 110 units and 220 units for industry I and Il respectively. (i) Total requirement of labour days. (iii) Total value addition, if labour cost is 7200 per labour day. (iv) Determine if the system viable using Hawkins - Simon conditions of viability? (12) (b) For a three-sector economy, the input-output coefficients, a are : (i) Determine the gross output for the three sectors when the final demand values for them are 21,000, 42,000 and 63,000 units respectively. ) Determine the new level of output if the final demand increases by 1500, 3000 and 4500 units. (c) A firm purchases two machines at a cost of 231,000 and $35,000 respectively. Both machines have a useful life of 4 years and have zero salvage values at the end of 4 years. Find the depreciation of each machine for each year using matrix notation if : (i) Both machines are depreciated by the straight-line method. (i) First machine is depreciated by straight-line method and second by the (6) sum of years digit method (d) A firm produces three products X, Y and Z processed on three machines M,, M, and M, before completion. M, can process 25 units of X or 50 units of Y or 75 units of Z per hour. Mi, can process 50 units of any one product per hour. M3 can process 50 or 25 or 100 units per hour of products X, Y and Z respectively. The processing hours available on machines M,, M, and M, are 12,12 and 13. respectively. Using matrix inverse or Cramer's rule, calculate how many units of three products can be produced (6) per day? 2. (a) (i) Find the elasticity of supply for the supply function: × = 2p? + 5, when p=3. (i) The demand x as a function of income y is given by 30x = 10 + 2y Calculate the value of income elasticity of demand when y = 250. (b) A firm has a demand curve x = 219 - 3p and average cost curve AC = 8 + * where p is the price per kg and x is the output (in kg). Determine the output at which the maximum profit can be earned. Calculate the corresponding maximum profit. (9) 7800 - 60t. Find the optimal time for replacement of the machine. (9) (d) The demand functions for two commodities are : (i) Calculate all the four partial elasticities of demand when P, = 5 and (i) Comment on the nature of commodities. (9) 3. (a) A production function is given by Q = 25 L'S KIs where I are the units of labour and K units of capital. (i Find the behaviour of the marginal product of each factor. (ii) What is the nature of returns to scale? (iii) What is the total reward of labour and capital if each factor is paid a price equal to its marginal product? (9) (b) Find the elasticity of substitution for the following function : (c) The price elasticity of demand of a commodity is E, = P/[(P - 1)(P - 2)]