Question

Write down the equation of a utility function and construct an indifference map that corresponds to each of the following case: -Bob always consumes beer and pizza in fixed proportions. Specifically, If Bob has 1 pizza, he consumes precisely 2 beers and additional beers represent no additional utility for Bob. Similarly, if Bob has 2 beers, he consumes precisely 1 pizza and additional pizzas represent no additional utility for Bob. In addition, when Bob has 4 pizzas and 10 beers, his utility is 32. **I understand that the formula for utility for perfect compliments is U(x,y)=min(aX,bY). How do you get the values a and b??? What do a and b represent in the equation??

Answer 1

The formula for utility for perfect compliments is U(P,B)= A*min(aP,bB),

It is given that: Bob always consumes beer and pizza in fixed proportions. Specifically, If Bob has 1 pizza, he consumes precisely 2 beers and additional beers represent no additional utility for Bob. This means For 1 unit of pizza he consumes 2 beer and hence he always prefer to consumes Pizza and Beer in the rate 1:2=> P/B = 1/2 . Hence kink of IC will occur at the point B = 2P

Also Note that, for utility function U(P,B)= A*min(aP,bB) kink will occur at the point wher aP = bB

Hence we have, B = 2P and bB = aP => b = 1 and a = 2

Hence we have U(P,B)= A*min(2P,B)

Also, when Bob has 4 pizzas and 10 beers, his utility is 32

=> U(4,10)= A*min(2*4,10) = 32

=> A*min(8,10) = 32

=> 8A = 32 => A = 4

Hence, the equation of a utility function is given by:

U(P,B)= 4*min(2P,B)

As discussed above b and a represents the fraction in which Beer and Pizza are consumed.