Question

show how the 'laffer curve' can be derived from the model of consumption-leisure choice.Why might an increase in the proportional tax rate lead to a reduction in tax revenue?

Answer 1

As we know that the “laffer curve” shows the relationship between the tax revenue and the size of the tax of tax rate. Now, we also know that the labor supply curve shows the relationship between “w” and the labor supplied. It is a backward bending, => initially when “SE > IE” it is upward sloping and when “IE” start dominating the “SE” it become backward bending.

Now, in the labor leisure choice problem the “tax revenue” is given by “w*t*H”, here “w” be the wage rate, “t” be the tax rate and “H” be the numbers of hors devoted to work. So, initially when “IE > SE”, as “t” increases => decrease in “w*(1-t)”, => “H” increases, => tax revenue also increases. Similarly, when “IE < SE”, as “t” increases => decrease in “w*(1-t)”, => “H” decreases, => tax revenue also decreases. So, diagrammatically it is given below.

So, here we can see that when “SE < IE”, as “t” increases implied increase in “tax revenue” and when “SE > IE” as “t” increases implied decrease in “tax revenue”, => here also the “laffer curve” is inverted “U” shape.

As we can see that when “SE > IE”, => as “t” increases implied the worker find it optimum to reduce their working hour also which implied “H” decreases, => decrease in “tax revenue” that is “W*t*H”.