Question

(i) (5%) Please define the Pareto efficiency. (ii) (10%) Figure 16.7 depicts the welfare impact of governmen equilibrium. Please use this graph to explain the efficiency chan decrease the tax from status quo. act of government's tax on the market the efficiency changes if government further Demand 16.7 2 (15%) Chapters 2 to 6 are analytical framework of consumer's theory. Please draw three graphs (in ppts of these chapters) that link "budget","preference (utility)" to "optimal choice of a rational consumer logically. You should put clear legends in the graphs and explain these graphs in reasonable details. 3 (20%) A consumer has a Cobb-Douglas utility function U(x1, x2) = Axibe and faces a budget constraint Pixi + p2X2 = m. w (10%) Please derive the individual demand function of Xi, using the first order condition (FOC) explained in the class (show your work step by step] (m) (5%) If a=0.6, b = 0.4, m = 80, p. = 5, P2 = 3, what is the optima p23, what is the optimal consumption bundle (iii) (5%) What is the demand function of xi look like? Draw it. 4 (20%) Elasticity is a very important economic concept. Fease write down and explain the definition of elasticity. (1) (5%) Please write down and explain (ii) (10%) Please derive the own price elastic (iii) (5%) What is the value of the elasticity the own price elasticity of linear demand function - a - bp value of the elasticity in (ii) when a = 10, b = 5,4"

Answer 1

Ans- Se pare to efficiency a locative lave to efficiency it is a state of allocation when it is imposside to make any one better off without make any one worde-off. Production Pareto efficieng Te is a state of Production when A A ADAP it is not possible to produce more of one good without deducing geantity of anomer good.

ce quantity a quantity (6) Since we know that gout Tex creatues The dead weight loss in economy. if govt. decrease The tax further, this will Leads to decrease in associated Tax generated dead weight loss. Comparing figure (a) and (6) Shows That decrease in dead weight loss foom B to B! and o to D' (it is easy to verify BY B' and DD. Decrecise in dead Loeight Loss increase the efficiency in economy. OUUUUUUUUUUU Ane (2) Let There are a goods (x, and x2) • p. and pe are prices of x, and X2 respectively, ana mis money income ofre Jerences are cobb-douglas.

SIC Budget Line XI o (c) goato (a) Shows The Burget dine which has usually mathmatica de presentation as Pixit P2 X 2 = m. goaph (b) Shows Ic curies for cobb- douglas Beyerences cobb-douglas preference refresented by Utility function U= XI. X2. gooph (C). Show The optimal Choice of consumer where Ic Carue is tangent To Budget dine at et

(Ans-3) (i com condition - mes= MRS= mox MUX2 = doldxl - PL dultxz Ka al b - where , а ь u= AXI X2 0-1 l = a Axi X2 a AXI X2 in a b-1 BAXI XZ GH Бех, - рә b-1 de=bAXI X2 bez b-bri a A.X2 - a-ati baxi . bz = - AX2 – bi bxp = ax = b bixi P2 = x2 = b bix! a pz Noco using Budget cquation pixi + b 2 x 2 =m bixit bz (6 bx ) = m pixit b bixi =

Pixi (It be = m Pix = m It ha CL 1 x = m asing (*1 ax2 = bi bx, D2 ax2 Pz = bxibi a X2 b2 = x1 b bi a bz X2 = XI b bi Pixit bz X2 = m. P 2 x + 2 = m bz X2=m a p2x₂ + 2x2 = m T p2x2 ( 1t a = m **

* 08 - Xog ." (6) Códs 08 = JS (1) . (+) (8 41) P2 ( 1+ a) Op+u Did m X2 = W = IX

X = 48 Table I + - + + dd funch + a a ro - NWS of xi + 5 9.6 O Š 16 24 48 x, Aneh Ans-4 Deyination of elasticity elasticity meciuris The Sensitivity of variables to an alteration in another Vasiable. Clasticity of demand meas wres how the amount of good changes conen its prices a changes. i q- a-bq

q=a-bp dq --b JP - a-bP at p=0 q=a at 90 pros a=bp = P = a elasticity of . = -b.a ها = -1 (111) a=10, b=5 9=7 excasticity = de elasti -boy - - 012 - 5 lol exausticity - 7 Cloti