INSTITUTE OF MANAGEMENT, NIRMA UNIVERSITY MBA (FT)- I (Batch ) : Term III (End Term Exam)

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1 INSTITUTE OF MANAGEMENT, NIRMA UNIVERSITY MBA (FT)- I (Batch ) : Term III (End Term Exam) Course : Managerial Economics Maximum Marks: 100 Date: Duration: 1 Hour Close Book Exam Instructions: 1. Answers should be short and specific. 2. Please start new answer on new page. Quesiton-1 (20 Marks) Examine the validity of the following statements. (Answer all questions) a) If the marginal utility of 5 units of the good X is 40, the total utility of 5 units of X must be 200. b) When a company advertises its product, it essentially makes its product more price elastic at a given price. c) If at a given price all individual demand curves are unit price elastic, the market demand curve must also be unit price elastic at that price. d) The slope of the budget line is given by the relative goods prices. e) In the short run, marginal fixed cost keeps falling as output expands. Answer: (a) Not True. MU is decreasing with increasing consumption. If MU=40 for 5 th Unit, then MU for previous units must be more than =MU 5th <MU 4th <MU 3rd <MU 2nd <MU 1st MU 5th +MU 4th +MU 3rd +MU 2nd +MU 1st >200 QED OR If MU of 5 units =40. That means Total Utility of 5 Units= Sum of MU of each of 5 units = MU 5th +MU 4th +MU 3rd +MU 2nd +MU 1st =40 Total Utility of 5 units =40 QED (b) Not True. When a company advertises its product, it expects consumers to buy product even though price is high OR at least more purchase at the current prices. Product becomes LESS elastic. (c) Not true. Market demand is less elastic than an individual demand. (d) True. By Definition, Budget Line = M=Px*Qx+Py*Qy, where X and Y are products, Qx and Qy are quantity consumed and Px and Py are prices of X and Y respectively. Slope =dqy/dqx = -Px/Py (e) Not True. In the short run, marginal fixed cost is NECESSARILY CONSTANT AND ZERO. Fixed cost being constant (at least in the short run), marginal fixed cost has to be zero. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Q2 (7+7=14 Marks) Answer the following providing brief explanation i) Goods X and Y are known to be substitutes. The price of Y increases. What would happen to the equilibrium price and quantity of the good X? ii) You are a distributor for tea and coffee. Tea and coffee are consumed in equal quantity by a consumer at an income of Rs. 100 though coffee prices are double the tea prices. If due to bumper crop, coffee prices fall to half of its original price, and due to rain failure

2 in Assam, tea prices are doubled then you would necessarily expect the demand for coffee to be four times the demand for tea Answer-02 (i) When the price of good Y goes up, demand for substitute would go up. Hence deamdn curve will shift to the right. Both, Equilibrium price and equilibrium quanitity go up. There is NO change in the supply curve of X. Commented [i1]: Price of X New Demand curve after Py increases E0 E1 Orignal Demand Curve Quantity of X (ii) At equilibrium, MU T MU C = PT PC P C MU C = P T MU T Originally, though Pc =2P T MUc=2 MU T, both are consumed in equal quantity. though both are equally consumed. Now, PC*= (1/2) PC and PT* = 2 PT PC*/PT* = (1/2)PC/ 2PT = (1/4) (PC/PT) At equilibrium, MU T* MU C* = PT* PC* P C* MU C* Pc MU C = = = P T* MU T* 4 pt 4*MU T

3 But MU is a concave function, increasing at a decreasing rate. Supposing, consumption of tea does not change. Then, MUT = MUT* 4 MUc* = MUc i.e. MU of coffee after the price change is four times. This can happen only if its consumption is reduced. But since utility function is concave reduction will not be four times. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Question-3 ( =24 Marks) The ABC Corporation has the following production function: Capital Labour The inputs (Labour: L, Capital: K) and Output (Q) prices (per unit) are P L = Rs. 10, P K = Rs. 20, P Q = Rs. 3 Based on this information, answer the following questions: a. Suppose capital is fixed at 5 units (K=5). Compute marginal and average physical products of labour. If the firm aims at maximum profit (minimum loss), how many units of labour it must employ? b. Suppose the firm is currently producing 50 units of output using K = 5 and L = 5. Is the firm using a least cost input technology? Why? c. Examine the returns to scale over the range of labour and capital shown in the table. Answer-3 (a) When Capital =5, MPL and APL are as follows: K L Total Product Average Product (L) Marginal product (L) (=32/2) 10 (=32-22) (=38/3) 6 (=38-32) (=44/4) 6 (=44-38) (=50/5) 6 (=50-44) (=54/6) 4 (54-50)

4 Optimal quantity of labour, for profit maximization is L=6. Because MPL is decreasing so if L=6 is good and acceptable, L<6 has to be acceptable and more. When 6 th labour is used, output is increased by 4 units whose value at P=3 is Rs th labour costs Rs 10. Hence MR(L=6) >MC(L=6). (b) Objective is to produce 50 units of output. Technology is already given in the table above. Decision problem is what is the optimal combination of K and L to rpduce 50 units of out put. And we get, (i) By reducing either input or both inputs one can not get 50 output. (ii) By reducing either L or K, and increasing the other, we CAN NOT get output of 50. E.g., (K,L) = (6,4) then output =48 <50. Similarly for (K,L) = (4,6) (iii) Hence, (K,L) = (5,5) is the least cost solution. (c) It is a constant returns to scale technology. E.g, (K,L) = (1,1) Output =10. Now (K,L) = (2,2) Then Output =20, exactly 100 % increase, the same increase as that of inputs. Now, if (K,L) = (3,3) implies inputs are increased by 50 % over (2,2). Then output =30. Exactly 50 % increase over 20. And so on. QED xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Question-4 (6+7+8=21 Marks) Let the demand function for sugar in a country be given as: Q = Y - 3P The supply curve is given by : Q = P Where Q is the quantity and P is the price of sugar; and Y is the real income of the consumers. Answer the following: (i) If Y is given to be 5000, what is the elasticity of demand for sugar at P = 30 (ii) If the government wants to introduce (specific) excise duty on sugar what would be the optimal duty? What is the equilibrium price? What is the loss in consumer surplus and producer surplus? (iii) If the income is expected to grow by 12% next year, what would be the optimal increase in profits next year? (i) If Y=5000, then, Q = *5000-3P = 510-3P ---(1) At P=30, Q = (2) Elasticity = (dq/dp)*(p/q) = (-3)*(30/420) = (-) (3/14) = (-) QED (ii) Originally, at equilibrium, Qs=Qd 510-3P = P 500= 3.2 P P= & Q=10+0.2P= * = = (1) Consumer Surplus = P=170 P= Supply Curve Q= P Q=10 Q=41.25 Consumer Surplus = ( ) *(1/2)*( ) = 41.25*0.5*13.75 = (1) Producer Surplus = (10*156.25)+(1/2)*( )* = (2) Total Surplus = CS+PS = = (3)

5 Now, Government introduces Rs. 1 as tax on each unit. This increases the marginal cost for the producer and hence supply curve will shift to the left. Original Supply Curve Q= P P = 5Q-50 With additional Rs. 1 as tax, P = 5Q P=5Q (1) (Remember that supply curve is a marginal cost curve. It gives additional cost for producing one extra unit. Hence, P=MC at any level of Q = 5Q-50. i.e. At this level of Q, to produce one more unit, and now Q+1 units to be produced, additional cost = 5Q-50. E.g, for Q= 20, P=MC = =50. That is, if at Q=20, now you want to produce one more unit, 21 st Unit, additional cost = 50.Rs. Then, to produce 22 nd unit, MC = 21*5-50 = 55 Rs. So when Rs.1 tax is imposed, for every unit to produce, Rs. 1 has to be paid to the government. Government is like factor of production. So P= MC=5Q-50+1 For new equilibrium, Demand Curve: Q =510-3 P P = 170-(1/3)Q Supply Curve : P= 5Q -49 Hence, 5Q-49 = 170-(1/3)Q (16/3)Q = 219 Q = 657/16 = And P = 5Q-49 = 5* = = P=170 P=156.3 Supply Curve Q= P Q=9.8 Q=41.06 Quantity has reduced from to Price has increased from to Consumer Surplus = (1/2)* 41.06*( ) = 41*7 = Loss in Consumer Surplus = =2.333 qed Original Producer Surplus =(10*156.25)+(1/2)*( )* = (2) New Producer Surplus = (9.8*156.3)+(1/2)*( )*156.3 = (3) Loss in Producer Surplus = = QED Total Loss in surplus = Loss in Consumer Surplus+Loss in Producer Surplus= = (iii) Originally, at equilibrium, Qs=Qd 510-3P = P 500= 3.2 P P= & Q=10+0.2P= * = = (3) Cost = Sum of all Marginal costs. Here, Supply curve=marginal cost curve is linear. At P=0, Q = 10 Hence, Sum of MC = Area of Rectangle ( 0 to 10, 0 to ) = Area of triangle (10 to 41.25, 0 to ) =( )*(1/2)*(156.25) = Total Producer Surplus=Profit = = Revenue = Q*P = 41.25* = Costs = = 2442 ( = (1/2)*( )* = ) ---(1) When income increases by 12 %, new income = Old Income*1.12 =5000*1.12 =5600

6 Now Demand == Qd =10+0.1*5600-3P = 570-3P = Qs = P Pnew=560/3.2 =175 and Qnew =10+0.2*175 = 45 Revenue = 45*175 = (1) Profit =new Producer Surplus = = Area Rectangle (0 to 10, 0 to 175)+Area of Triangle (10 to 45, 0 to 175) = 10*175+ (1/2)*(45-10)*(175) = = Costs = = (1) Increase in Profits = = QED xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Question-5 Given the total cost function TC = Q - 9 Q Q 3 ( =21 Marks) Where, TC = Total Cost (in thousands of rupees) and Q is the output (in thousands) Determine: (a) The equation for each total and per unit cost function (TVC,FC,AFC,AVC, AC and MC) (b) The lowest price of the output that would allow the firm to break even (c) The lowest price of output that would allow the firm to cover average variable cost (d) The output rate at which the average cost is minimized. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Ans. 05 TC = Q - 9 Q Q 3 Where, TC = Total Cost (in thousands of rupees) and Q is the output (in thousands) (a) AC = TC/Q = 1000/Q Q+0.25*Q (1) (b) FC = 1000 AFC = 1000/Q ----(2) (c) VC = 200Q-9Q Q 3 AVC = Q (3) (d) MC = d(tc)/q = Q +0.75Q (4) 2. For break even, P=AC At lowest price AC is minimum. At minimum AC, AC=MC 1000/Q+200-9Q+0.25Q 2 = Q+0.75Q Q 3-9Q = 0 Q 3-18Q =0 Q 2 (Q-18)=2000 Q=22 (Approx.) Price when Q=22 P=MC =200-18Q +0.75Q * *22*22=P=167 QED 3. To cover Average variable Cost MC=AVC Q+0.25Q 2 = Q+0.75Q Q 2 = 9Q Q=18 P =AVC = *9+0.25*18*18 = 119 QED 4. Lowest price to break even = Minimum AC. Answer is in Part (b) above Q=22 (approx..) Xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx