Question

Question 2:Donny’s monthly budget for Coffee and Muffins is 60 and the prices of those two goods are pC=2 and pM=4, respectively.

(a) Make a properly labeled diagram illustrating Donny’s budget constraint withCon the horizontal axis and M on the vertical axis. Indicate the area corresponding to the set of bundles(C,M)that Donny can afford.

(b) On the same diagram, illustrate Donny’s budget constraint if pM falls from 4 to 2.Up until this point it is impossible to predict what Donny will purchase without knowing his preferences.

(c) Suppose Donny views Coffee and Muffins as perfect substitutes (he is always willing to trade one C for one M). Which bundle of the two goods will he purchase, assuming pC=2 and pM=4?

(d) Suppose Donny views Coffee and Muffins as perfect complements (he always has to consume one C with one M to obtain any utility). Which bundle of the two goods will he purchase, assuming pC=2 and pM=4?

(e) In which case of preferences (perfect substitutes or perfect complements) would Donny benefit more from the price decrease of pM=4 topM=2?

Answer 1

Questions Donny's monthly budget for coffee and Muffin and the puces of two goods are pe=2 and PM 24 respectively Now suppose we denote quantity of coffee by and quantity of muffin by M tue in come I=60 a Huce Donny's budg it constraint with C on the horizontal an is and M on the vatical anis will be t I = e Pet MPM ang 60 = act 4M et Donny consues only his band horizontal constraint will be budg it con straint 7 coffee and no muffin, then in tucept of the budget [ substitute M20 in the =) 60 5 20 +4 (0) E) C = 30 and it Donny consues only muffin and no coffice then by substituting Co in the budget constraint we will get the uutical in th cept of the budg it. constraint. - Hunce, 60=210) + 4 M. _M _ ē IS . Now, by Joining horizontal and vutical intucept we can get Bonny's budget Constaint AB. Scanned with CamScanner

AT 3097 C 30 This, the Shaded area represents the area Corris ponding to the set of bundles (CIM) that Donry Can afford.. then b. It Pim falls to 2 from 4 his budget constraint will bet SON - 60 3 20 + 2 m Then his ventical in Ancept of the budget om line will be ! [ substitute C-o intretano the budget Constant I 60= 2(0) + 2M M2.30 Tu jh TCS Scan Scanned with CamScanner

in ter cept remains unclouged at @= 30, Horizontal in tu cept nemains unclog Huce the budget line will she rotate outward 610mAb to A'Brien I suppose Donny views Coffee and muffins as Putect substituty. and he is wilay to trade one e for one M. Hunce utility fonction for pufect sub's to fetc will be U= a et b m As he is willing to tade, one e for one, M hence here i a = 1 and b = 1 n a Hace ucetm Now, Hue Marginal utility of -Bau a je MUC won and marginal utility of M ic. MUM Also Pe=2 and Pm = 4 Now moe- 1 - 0.5 a pe ... Mum and 1.20.25 and w toit g As muc mun. they Donny will puclause PCT PM only coffice and no Muftica. Scanned with CamScanner

to Con all his in come in So, Consmen will spend a On Coffee and by substituting pend m=0 g and the budget constaint we gutt # We gut! 1 60 = 20 +4 (o 2) C = 30 12 Huice to he will pum chase the (cm) = (308) the bundle a an suppose Donny vicws coffee and muffins I pufect complements (and he has con sme one C with one in to obtain any utlity) to consme one Now, his utility function will be con U = min lapbm) a the as Obtain he has to one e consue thes, one m a=1 to with and b=1, Now = min (e, m) Hure, Wility manimisation Condition that bonny Consmes, C and M in a manner that eam requius such in the budget Hince substituting C= m constaint we get, . .. scanned with Cam Seamer

60 = 2ė tym _ =20 +4C to be es 10 As, mze Hunce - n=10 Hence he will pm chase bundle . (CM) = (10, 10) e2 af Pin decreases from Pm = 4 to Pm=2, - this, in case of pufect substitutes, - muca 1 = 0.25 - and MUM - 1 0 .5 _pin As Muc - mum he will pmclase both PC PM the commodities in equal amount, hence he will pm chase 15 mits of e and 15 mits of M, or (CM) - (15,15) In case or putect complements, Ib Pm=2, budget constaint will be 603 że + 2M substituting C=M we get 60=20 + 2C =) 60 = 40 Ca 15 - as cam, m=15, hence he will pm chase Cem) - (15,15 ) Hule Donny gits equal benefit from both preferences for spmon decreases to 2 from 4.