Homework Answers
Um = c1+c2
Uj = min[2c1,c2]
m1 = 40 m2 = 272 for both matt (m) and jenny (j) and r = 0.2. therefore, their NPV of income say m = m1+m2/(1+r) = 40+272/1.2 = 266.66
NPV of total consumption would be c1 + c2/1.2
therefore BC: c1 + c2/1.2 = 266.66
A) optimal combination for Matt.
maximise Um = c1+c2 s.t c1 + c2/1.2 = 266.66
since from BC we can see that, price of c1 = 1 and price of c2 = 1/1.2 = 0.833
price of c2 is less than price of c1, and ci and c2 are perfet substitutes, matt will choose only c2. thus, c1 = 0
and c2 = 266.66*1.2 = 319.992
B) for jenny
maximise Uj = min[2c1,c2] s.t c1 + c2/1.2 = 266.66
since 2c1 and c2 are perfect comeplements used in ratio 2c1 = c2 that is c1/c2 = 1/2
putting this in BC we have c1 + 2c1/1.2 = 266.66
1.2c1+2c1 = 266.66*1.2
3.2c1 = 319.992
c1 = 99.99
c2 = 2c1 = 199.95
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