Consider the static labour-leisure model from the notes, with one change: households earn an overtime wage wt > wt if they work more than 0 < h < h hours. 

(a) Illustrate, in a properly labelled diagram, the household budget constraint for this problem. Explain what happens to this constraint when the overtime wage wt in- creases. 

(b) Write down the household's utility maximisation problem. 

(c) Illustrate, in a properly labelled diagram, the household's optimal labour-leisure choice in the case in which it does not work any overtime. 

(d) Evaluate the following claim: "An increase in overtime wages must increase household labour supply". 2. Consider the static labour-leisure model from the notes, with one change: a government levies a proportional sales tax of  > 0 per unit of consumption good. 

(a) Illustrate, in a properly labelled diagram, the household budget constraint for this problem. Explain what happens to this constraint when the tax  increases. 

(b) Write down the household's utility maximisation problem. 

(c) Write down the Lagrangian for the household's problem, derive its first-order condi- tions, solve for the tangency condition and illustrate in a diagram. (d) Evaluate the following claim: "An increase in consumption taxes must decrease house- hold consumption".