Consider the labour-leisure choice problem, where individual faces decision how to allocate time between work and leisure. Supplying labour services in the labour market earn her an income which can be used to buy goods and services, but leisure is also a good and it can be consumed only by not working. Individual has T hours to allocate between work, L, and leisure, R. Money income equals the wage rate, w, times the number of hours worked. Thus, the individual maximizes U( MR) subject to T=L+R, where M=WL, or L= M/w. (a) Solve the problem by transforming it into an unconstrained optimization problem with one variable. (Hint: in utility function, substitute for Mas function of R.) Interpret the FONC. 4 (6) Is / are the second-order condition(s) satisfied? (c) Show that the Lagrange method leads to the same solution. (d) Interpret the Lagrange multiplier. Consider the labour-leisure choice problem, where individual faces decision how to allocate time between work and leisure. Supplying labour services in the labour market earn her an income which can be used to buy goods and services, but leisure is also a good and it can be consumed only by not working. Individual has T hours to allocate between work, L, and leisure, R. Money income equals the wage rate, w, times the number of hours worked. Thus, the individual maximizes U( MR) subject to T=L+R, where M=WL, or L= M/w. (a) Solve the problem by transforming it into an unconstrained optimization problem with one variable. (Hint: in utility function, substitute for Mas function of R.) Interpret the FONC. 4 (6) Is / are the second-order condition(s) satisfied? (c) Show that the Lagrange method leads to the same solution. (d) Interpret the Lagrange multiplier