# Chapter 3

1.5 If the neutral product is on the vertical axis, the indifference curves are parallel vertical lines.

2.2 Sofia’s indifference curves are right angles (as in panel b of Figure 3.5 ). Her utility function is $U=\text{min}(H,W),$[&U|=|~rom~min~normal~(H, W),~norm~&] where

*min*means the minimum of the two arguments,`H`is the number of units of hot dogs, and`W`is the number of units of whipped cream.2.4 If we apply the transformation function $F(x)={x}^{\rho}$[&F(x)|=|x^{|rho|}&] to the original utility function, the new utility function $V({q}_{1},{q}_{2})=F(U({q}_{1},{q}_{2}))={[{({q}_{1}^{\rho}+{q}_{2}^{\rho})}^{1/\rho}]}^{\rho}={q}_{1}^{\rho}+{q}_{2}^{\rho},$[&V(q_{1}, q_{2})|=|F(U(q_{1}, q_{2}))|=|[(q_{1}^{|rho|}|+|q_{2}^{|rho|})^{1/|rho|}]^{|rho|}&][&|=|q_{1}^{|rho|}|+|q_{2}^{|rho|},&] which has the same preference properties ...

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