BA (Honours) Economics Past Paper PDF (BECC-102, December 2021)

No. of Printed Pages : 8 BECC-102 B.A. (HONOURS) ECONOMICS (BAECH) Term-End Examination December, 2021 BECC-102 : MATHEMATICAL METHODS IN ECONOMICS – I Time : 3 hours...

No. of Printed Pages : 8 BECC-102 B.A. (HONOURS) ECONOMICS (BAECH) Term-End Examination December, 2021 BECC-102 : MATHEMATICAL METHODS IN ECONOMICS – I Time : 3 hours Maximum Marks : 100 Note : Answer questions from each section as directed. SECTION A Answer any two questions from this section. 220=40 1. (a) Show that when profit is maximised, MC P= ,  1  1       d where  = elasticity of demand. d (b) A firm has a demand and total cost function given by the respective equations P = 300 – Q and TC = 800 + 2Q. Find the price, quantity and  at which d profit is maximised. BECC-102 1 P.T.O. 2. The demand and supply functions for a good at time t are given as : Qdt = 125 – 2Pt Qst = – 50 + 1.5Pt–1 (a) State the equilibrium condition, hence deduce a difference equation in P. (b) Solve the difference equation to find the equilibrium price and quantity. 3. (a) Find the gradient of the line 2x – 3y + 1 = 0 and the coordinates of the points where it cuts the axes. (b) Show that the line joining the points (p, q) and (kp, kq) passes through the origin, whatever the values of p, q and k. 4. (a) The supply and demand functions for a product are : qs = p2 – 400, and qd = p2 – 40p + 2600 Determine the market equilibrium price and quantity. (b) The demand function for a particular product is q = f(p) = 2400 – 15p, where q is stated in units and p in rupees. Determine the revenue function. What is the total revenue when the price is < 50 ? What is the quantity demanded at this price ? At what price is the total revenue maximised ? BECC-102 2  SECTION B Answer any four questions from this section. 412=48 5. Capital K and Labour L in an economy are given by the linear functions K = 2 + 3t, L = 1 + 4t, where t denotes time. Find the rate of change with respect to time. 6. If the marginal revenue function is ab ab MR = – c, show that p = – c is ( x  b) 2 ( x  b) the demand function. Here p is price and x is quantity demanded. 7. Discuss the basic set-up of the Cobweb model. 8. (a) Suppose A = {x, y, z}. List all the subsets of A. (b) What is an injective function ? (c) What do you understand by Cartesian product ? 9. (a) Explain the following : (i) Theorem (ii) Proof (b) Briefly discuss the various types of proof. 10. Examine the continuity of the functions : (1 – x 2 ) (a) y = 1–x (b) y = x (x + 1), for x > 0 BECC-102 3 P.T.O.  SECTION C Answer all questions from this section. 26=12 11. Evaluate : x2 – x – 2 (a) lim x2 x (x – 2) x 3 – x 2 – 9x  9 (b) lim x 3 x2 – x – 6 12. Explain : (a) Point of inflexion (b) Order of a difference equation BECC-102 4  ~r.B©.gr.gr.-102 ~r.E. (Am°Zg©) AW©emñÌ (~r.E.B©.gr.EM.) gÌm§V narjm {Xgå~a, 2021 ~r.B©.gr.gr.-102 : AW©emñÌ _| J{UVr` {d{Y`m± – I g_` : 3 KÊQ>o A{YH$V_ A§H$ : 100 ZmoQ> : àË`oH$ ^mJ go àíZm| Ho$ CÎma {ZX}emZwgma Xr{OE & ^mJ H$ Bg ^mJ go {H$Ýht Xmo àíZm| Ho$ CÎma Xr{OE & 220=40 1. (H$) Xem©BE {H$ O~ bm^ A{YH$V_ hmoVm h¡, V~ MC P= ,   1  1   d    Ohm±  d _m±J H$s bmoM h¡ & (I) EH$ \$_© H$s _m±J VWm Hw$b bmJV \$bZ {ZåZ g_rH$aU Ûmam {XE JE h¢ : P = 300 – Q VWm TC = 800 + 2Q H$s_V, n[a_mU VWm _m±J H$s bmoM (d) kmV H$s{OE Ohm± bm^ A{YH$V_ h¡ & BECC-102 5 P.T.O. 2. g_` t na {H$gr gm_J«r H$m _m±J VWm Amny{V© \$bZ h¡ : Qdt = 125 – 2Pt Qst = – 50 + 1.5Pt–1 (H$) g§VwbZ pñW{V H$s ì`m»`m H$s{OE Am¡a P H$m EH$ A§Va g_rH$aU ì`wËnÞ H$s{OE & (I) g§VwbZ H$s_V VWm n[a_mU kmV H$aZo Ho$ {bE A§Va g_rH$aU hb H$s{OE & 3. (H$) aoIm 2x – 3y + 1 = 0 H$s T>mb (àdUVm) kmV H$s{OE Am¡a CZ {~ÝXþAm| Ho$ {ZX}em§H$ kmV H$s{OE Ohm± aoIm Ajm| H$mo H$mQ>Vr h¡ & (I) Xem©BE {H$ {~ÝXþ (p, q) VWm (kp, kq) H$mo {_bmZo dmbr aoIm _yb-{~ÝXþ go JwµOaVr h¡, Mmho p, q Am¡a k H$m _mZ Hw$N> ^r hm| & 4. (H$) {H$gr CËnmX Ho$ Amny{V© VWm _m±J \$bZ h¢ : qs = p2 – 400, VWm qd = p2 – 40p + 2600 ~mµOma g§VwbZ H$s_V VWm n[a_mU kmV H$s{OE & (I) {H$gr {deof CËnmX H$m _m±J \$bZ h¡ q = f(p) = 2400 – 15p, Ohm± q H$mo BH$mB`m| _| Xem©`m J`m h¡ Am¡a p én`m| _| & amOñd \$bZ kmV H$s{OE & O~ H$s_V < 50 h¡ Vmo Hw$b amOñd {H$VZm hmoJm ? Bg H$s_V na {H$VZm n[a_mU _m±J {H$`m OmEJm ? {H$g H$s_V na Hw$b amOñd A{YH$V_ hmoJm ? BECC-102 6  ^mJ I Bg ^mJ go {H$Ýht Mma àíZm| Ho$ CÎma Xr{OE & 412=48 5. {H$gr AW©ì`dñWm _| ny±Or K VWm l_ L {ZåZ{b{IV a¡{IH$ \$bZ Ûmam {X`m J`m h¡ : K = 2 + 3t, L = 1 + 4t, Ohm± t g_` H$mo Xem©Vm h¡ & g_` go g§~§{YV n[adV©Z Xa kmV H$s{OE & 6. `{X gr_m§V amOñd (marginal revenue) \$bZ ab ab MR = 2 –c h¡, Vmo Xem©BE {H$ p= –c ( x  b) ( x  b) _m±J \$bZ h¡ & `hm± p H$s_V h¡ Am¡a x _m±J H$m n[a_mU h¡ & 7. _H$‹S> Omb {ZXe© (H$m°~do~ _m°S>b) Ho$ _yb^yV T>m±Mo H$s MMm© H$s{OE & 8. (H$) _mZ br{OE A = {x, y, z}. A Ho$ g^r Cng_wƒ`m| H$s Vm{bH$m (list) ~ZmBE & (I) EH¡$H$s \$bZ (injective function) Š`m h¡ ? (J) H$mVu` JwUZ (Cartesian product) go Amn Š`m g_PVo h¢ ? 9. (H$) {ZåZ{b{IV H$s ì`m»`m H$s{OE : (i) à_o` (ii) Cnn{Îm (I) Cnn{Îm Ho$ {d{^Þ àH$mam| H$s g§jon _| MMm© H$s{OE & 10. {ZåZ{b{IV \$bZm| Ho$ gm§VË` H$s Om±M H$s{OE : (1 – x 2 ) (H$) y= 1–x (I) y = x (x + 1), x > 0 Ho$ {bE BECC-102 7 P.T.O.  ^mJ J Bg ^mJ go g^r àíZm| Ho$ CÎma Xr{OE & 26=12 11. kmV H$s{OE : x2 – x – 2 (H$) lim x2 x (x – 2) x 3 – x 2 – 9x  9 (I) lim x 3 x2 – x – 6 12. g_PmBE : (H$) Z{Vn[adV©Z {~ÝXþ (Point of inflexion) (I) A§Va g_rH$aU H$s KmV BECC-102 8