Question

1. (Health Economics) The following questions relate to the Grossman model
   1. What are the two goods utility depends on?
   2. What are the two main constraints?
   3. Draw a graph showing the labor-leisure tradeoff. Now show what happens when health improves (e.g. overcame a serious illness).
   4. Draw a graph of the MEC (marginal efficiency of health capital curve). Show how aging affects the optimal choice of Health.

Answer 1

By this example...........................

put

The constraint is given as .

(a) For the given values of P and W, we have or as the constraint. The utility function is . The lagrangian to maximize the utility with the given constraint will be . The FOCs are below.

or or or .

or or or or .

or or or .

Comparing the first two FOCs, we have or or , which is the optimal combination of consumption and leisure. Putting that in the third FOC, we have or , and as , thus or .

Hence, the optimal level of consumption is 120 units, while the optimal amount of leisure is 12 hours. She is working hours a day.

(b) The utility function would be . The budget constraint would be or , as P is 1. The lagrangian would be
I = a * In (C) + (1-0)ln ( L ) + λ(2411-C-II-L)
. The FOCs would be as below.

or or or .

or or or or .

or or $(2411-C-WL)=0$ or .

Comparing the first two FOCs, we have or or
(1 - a)
, which is the optimal combination of C and L. Putting it in the third FOC, we have
(1- a) 2411.
or
(1- a)
or or , and since , we have or .

The parameter alpha is the preference of consumption against leasure. As alpha tends to 1, the preference to consumption is more and preference to leasure is less, and vice cersa as alpha tends to 0. This can also be seen in the equilibrium bundles of C and L.

(c) We have and . The effect of alpha on C would be
(0241 do
or . The effect of alpha on L would be or .

As can be seen, as alpha increases marginally, optimal C would increase by 24W, while optimal L would decrease by -24. It is as alpha denotes the preference towards consumption.

(d) The graph would be as below.

As W increase, Anne's budget lines moves to right in an angular movement. Also, except zero consumption and L=24 point, all the points in the new budget line are more preferred than before, as they have more C for the same L than before.