Question

In: Economics

Per usual, assume that the representative consumer, both in Europe and in the US, has a...

Per usual, assume that the representative consumer, both in Europe and in the US, has a utility function given by u(c,l) . As for their budget constraints, assume that the real wage in both Europe and the US equals w and that there does not exist physical capital. Rather than assume the presence of lump-sum taxes, assume instead that there exists an income tax so that the relevant real wage is now the after-tax real wage, (1i )w where the subscript i allows for a different tax rate in Europe rather than the US. Show how this simple model can explain the difference in hours worked. What does it imply about the possibility of any differences in consumption between Europe and the US?

Solutions

Expert Solution

Consider the given problem here the representative consumer in both “Europe” and in the “US” has a utility function given by, “U=U(C, L). In both countries have the same real wage “w” but different income tax rate “ti”. So the equation of the budget line is given by, “C + w*(1-ti)*L = w*(1-ti)*T, here “T=total time availability”.

Let’s assume that both the consumer have the same utility function, the utility maximization problem of the consumer is given below.

=> Max U=U(C, L) sub to “C + w*(1-ti)*L = w*(1-ti)*T”, where “i” represents “Europe” and “US”.

So, we can see that there is only a one difference which is the tax rate, apart from the “ti” everything is same to each country. So, if we maximize it we will get the optimum solution given below.

=> C*(w, ti) and L*(w, ti). Now because in both country have different “tax rate”, => both the country have different “after tax real wage”, => both country have different “consumption “ and “working” choice, even if both have same preference and same real wage.

We can explain this through “IE=income effect” and “SE=substitution effect” by using fig.

Let’s assume that in both the country the actual real wage is comparatively low and “US’ have low tax rate compared to “Europe”, => “US” have higher “after tax wage” compared to “Europe”. So, in the 1st fig the “black budget line” correspond to “Europe” and “Red budget line” correspond to “US”, We can see that “US” have higher level of consumption choice (C2 > C1) and lower level of leisure choice, => they devote more time to “working hour” compared to “European” worker(L2 < L1, => H2 > H1).

We can explain this through the “IE” and “SE”, as we know that “IE” and “SE” effect’s adversely in this model.

Here in both the country have comparatively lower real wage, => “SE” is more stronger compared to “IE”, => higher real wage encourage the worker to work more and enjoy less leisure, that why as the “US” workers are getting more “after tax real wage”, will devote more time towards “work”, => they will also consume more compared to “European” workers.

Let’s assume that in both the country have comparatively high the actual real wage, and “US’ have low tax rate compared to “Europe”, => “US” have higher “after tax wage” compared to “Europe”. So, in the 2nd fig the “black budget line” correspond to “Europe” and “Red budget line” correspond to “US”, We can see that “US” have higher level of consumption choice (C2 > C1) and higher level of leisure choice, => they devote less time to “working hour” compared to “European” worker(L2 > L1, => H2 < H1).

We can explain this through the “IE” and “SE”, as we know that “IE” and “SE” effect’s adversely in this model.

Here in both the country have comparatively high real wage, => “SE” is less stronger compared to “IE”, => higher real wage encourage the worker to work less and enjoy more leisure, that why as the “US” workers are getting more “after tax real wage”, will devote less time towards “work”, => they will also consume more compared to “European” workers.

So we can see that in both the cases both the country have different choice and these difference is coming only because of the tax rate “ti”, because both country have different tax rate, => both the country have different after tax wage rate. Now, because of this different “after tax wage” leads to different choice.

We can see that in different situation “US” worker have different choice towards “L” and “H” depending on the real wage, but in both cases they consume always more compared to the “European” worker, because here we assumed that “US” have lower tax rate compared to “Europe”.


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