3. In the theoretical Malthusian model, the law of motion of population is given by Lt+1 = nt Lt. However, we use the equation Lt+1 = 2(AX)a (L₁)¹-a to solve the model. Explain how the two equations relate, and why we can't use the first one to solve for the evolution of population directly. 4. Suppose the utility function of parents is given by u(c, n, h) = (1 - y) lnc + y(ln n + Bln h), where c is consumption, n is number of children, and h is their human capital. As in the model we saw in class, h = h(e, g) where e is the level of education of the child and g is the growth rate of technology. Interpret the parameter 3. What does it mean for the cross derivative of h with respect to education and technology growth to be positive (heg > 0)?
3. In the theoretical Malthusian model, the law of motion of population is given by Lt+1 = nt Lt. However, we use the equation Lt+1 = 2(AX)a (L₁)¹-a to solve the model. Explain how the two equations relate, and why we can't use the first one to solve for the evolution of population directly. 4. Suppose the utility function of parents is given by u(c, n, h) = (1 - y) lnc + y(ln n + Bln h), where c is consumption, n is number of children, and h is their human capital. As in the model we saw in class, h = h(e, g) where e is the level of education of the child and g is the growth rate of technology. Interpret the parameter 3. What does it mean for the cross derivative of h with respect to education and technology growth to be positive (heg > 0)?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:3. In the theoretical Malthusian model, the law of motion of population is given by Lt+1 = nt Lt.
However, we use the equation Lt+1 = 2(AX)a (L₁)¹-a to solve the model. Explain how the
two equations relate, and why we can't use the first one to solve for the evolution of population
directly.
4. Suppose the utility function of parents is given by u(c, n, h) = (1 - y) lnc + y(ln n + Bln h),
where c is consumption, n is number of children, and h is their human capital. As in the model
we saw in class, h = h(e, g) where e is the level of education of the child and g is the growth
rate of technology. Interpret the parameter 3. What does it mean for the cross derivative of
h with respect to education and technology growth to be positive (heg > 0)?
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