Question

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13. Aji's utility function for Blueberry (b) and Raspberry (r) is given as follows: U = f(b,r); Budget constraint: 100 = 4b + 5r a. Graph the budget constraint, labeling all relevant items, put Blueberry in the horizontal axis and Raspberry on the Vertical axis. For each bundle given below, is the bundle feasible for this budget constraint? What can you say about the bundle possibly being the utility-maximizing bundle? b. Bundle (10, 15) C. Bundle (7, 13) d. Bundle (5, 16)

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Answer 1

18 Aje's ability function for Blue borry (b) is quesas A and Raspberry (0) is given by ? U= f (b, 2); Budget constraint: 100=4bt so a Nows it tol Plot Bad Blueberry in the horizontal ane's and Rasp borry on entical aris, then horizontal in tucepit of the budget constraint will be found by substitueing 820 in the budget constraint. Hace 100 = 4b +(5*) =) b=25 Now, Nutical in Ancept of the budget line will be bound by substituting b=0 in the budget Constaint. Hace 100= 4b +50 - 100 = (4 *0) +57 = = 20 Now, by by stubstful substitut Joinery ban Joining b=25 and 8= 20 We will get Asi's budget constaint AB. gut canned with CamScanner

q Raspbury (0) 20 XB 25 Blueberry (6) b) Now for the bude (10, 15) price of b is $4 , herce 10 brudles cost * (10xy) - $40 Price of bon is $5, hence 15 bradl mits cost $(1585) =$75 Hence total budget by consring louits of band 15 mits of a will be $ (40+75) = $115 As total budget $115 is greath them the manner allowable budget of $1.00, hence the budle is not feasible. cs Scanned with CamScanner

Bundle (7,13] consning 7 mits of blueberry cost of Now to stal will be s $17x4) = $28 And total cost of consuming 13 mits of Raspberry will be r (13x5)=465 Now to tal budget of consuming 7 mits of blueberry and 13 mits of Raspberry will be a $(28+65) 893 as total cost of consuming the budle (7, 13) ic $93 is - less than the manninum allowable budget 1.6$100 herce the bundle is beasible.but not optimal. d Now, for the Bundle (5,16), total cost of consming . 5 mits of b will be $5x4) = $20 and total cost of consming 16 mits of a will bet - $ (16 x 5) - $ 80 Hace to tal budget of consming 5 mits of Benel 16 muits of R will be = $ (80+20) = $100. As total cost of consuming the bulle (5,16) ic & 100 i equal to the mannen allowable budget iic $ 100. hence the burdle i feasible Here only the badle (5,16) is utility maninising bradle be cause et exhausts the total allowab.ee Cadastre si mith $ 100.