Question

1)Suppose that the utility function of a household is: U(c,l) = 2c +4l What is the marginal rate of substitution between consumption and leisure?

2)Y = 8L^0.5 What is the marginal product of labour when there are 4 employees in the economy?

3)Suppose that a household must pay $100 in taxes and can work a maximum of 16 hours at a wage of $10 per hour. What is the maximum this household can consume in this period?

Answer 1

1) Marginal rate of substitution between consumption and leisure = Marginal utility of leisure/Marginal utility of consumption
Marginal utility of consumption =

Marginal utility of leisure =

So, Marginal rate of substitution between consumption and leisure = 4/2 = 2

2) Marginal product of labour, MPL = dY/dL = (8)(0.5)[L^(0.5-1)] = 4(L^-0.5) = 4/(L^0.5)
At L = 4, MPL = 4/(L^0.5) = 4/(4^0.5) = 4/2 = 2
So, MPL = 2

3) Maximum consumption = [wage*maximum working hours] - taxes = (10*16) - 100 = 160 - 100 = $60
So, $60 is the maximum this household can consume in this period.