Question

vorul Consumer theory begins with a discussion of consumer preferences - and there sure are a lot of them. In this assignment, you're tasked with developing a one-page "infographic" or "poster" that depicts the graphical representation (ie, indifference curves) of utility max of the following types types of preferences: 1. imperfect substitutes with a budget constraint and utility max. Next to it, summarize how you would find the utility max point (should include marginal utility per dollar spent). 2. perfect substitutes with a budget constraint and utility max. Next to it, summarize how you would find the utility max point (should include marginal utility per dollar spent). 3. perfect complements with a budget constraint and utility max. Next to it, summarize how you would find the utility max point (should include marginal utility per dollar spent...

Answer 1

In general, any utility function that produces non-linear and downward sloping indifferen -ce Curves will feature Imperfect substitutability between goods. By considering only good, I we're implicitly assuning "more is preferred to ess", os posituie marginal nticity for each good or in other words a look at the marginal rate of substitution (MRS) and see if it depends on the quantity of ether good. & it does then there is imperfect substitutabilly Enambles : (1) Quasi-linear utility, uex,y) = V(x) + 4. where vex) is non linear in x , encomple. VCO) = vac (2) Coo6- Douglare: Ulry) = xy P r & p70 Answer!) Budget constraint be.x+ Py y=h where Pa= Price of gooda Py = Price of goody M= money income MRS = 24/ax - mun xud y _ x 14 | aulay muy ß y Blah B (2)

MRS = opeimatily arises where, d y = that is Px- a of Be Budget slope of line target or slope of indiffernce L aurie on Incliftersce Curve Budget line (Interids solution) is to Equilibrium point = E Equilibrium Bundle= (x + y) - C o x* m/Be gooda Conditions MRs> ege ie (MRS) (by) Consume more (MRS= P2) of good MRS < Ph (MRS) (Py) < Pu consime more of good y so that mu of good & Tau than MRS increads as MRS= (mun 17 (muyt

Ans (2) Perfect lubstitute . u(x,y) = ax+by MR Say = aux muna Budget Cowansainl: Px. (%) + Vy (Y) =M Equilibrium conditions: (1) MRS = Pu (not enith or partially Py esist here) - Corner suktion may be enist if Pu>py → consume goody Pa<ly Consume good & goody mey (MRS - Pose) - consumes anywhere in the line in the -Budget line goody TY MRSxlu i ly A co only good x. Budet liñe Mfryt r y gree Type gode o r goods

(Ans-3) Perfect Complement (used together Ulex,y) = min (algy) Oblimality arises at kink where (x=y Budget Combaint m= x P + y Py . Equilibrium always cant at sani librium) IC Equilibrius bine S mer goods