Matt gets utility from leisure (Le) and consumption (X) and his preferences can be represented by...

 

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Matt gets utility from leisure (Le) and consumption (X) and his preferences can be represented by the following utility function, U(Le, X)=(¹/2+X¹/2)2. Matt has T hours per day to devote to working (La) or leisure (Le). The price of consumption is p, Matt earns w per hour and his nonlabor income is Io. What are Matt's ordinary demand functions, Le* (w, p, Io) and X-(w, p, Io), and labor supply function, La* (w, p, Io)? Will Matt work more or less if he wins the lottery? Prove your answer carefully. Matt gets utility from leisure (Le) and consumption (X) and his preferences can be represented by the following utility function, U(Le, X)=(¹/2+X¹/2)2. Matt has T hours per day to devote to working (La) or leisure (Le). The price of consumption is p, Matt earns w per hour and his nonlabor income is Io. What are Matt's ordinary demand functions, Le* (w, p, Io) and X-(w, p, Io), and labor supply function, La* (w, p, Io)? Will Matt work more or less if he wins the lottery? Prove your answer carefully.