Question

(10 pts) In the Grossman model, the individual maximizes U-U(H,Z), where H- HITH, M) and Z Z(T2, J; subject to the constraints that: a. what does H = H (T, M) represent? b. What does Z Z (T, J) represent? c. Identify and explain the first constraint. d. Identify and explain the second constraint. e. Suppose an individual is seriously injured and out of work for six months. His disability benefits replace only 2/3 of his pre-injury wage. How does the injury affect each constraint? What is the most likely effect on Z? Explain

Answer 1

a) H is considered to be stock of health. This H is a function of T^h and M.

  T^h is considered to be the time input and M is considered to be the good that contributes to the total investment in health.

b) Z is considered to be aggregate of commodities consumed beside health. It is a function of T^z and J.

T^z is again a time input and J is the inputs required in production of good Z.

c) The first constraint is also knows as the "TIME CONSTRAINT" where T^z and T^h are already explained above. T^w is considered to be the time lost from performing activities (market and non-market) due to illness.

This three components add up to total amount of time available.

d) The second constraint is the "GOODS BUDGET CONSTRAINT". p_mM and p_jJ are the total value of goods M and J respectively. T^w is hours of work and W is wage rate. So, WT^w is the total value of work.

e) Since due to injury time is lost  T^w goes up in the first constraint leading to reduction in T^z and T^h as total time is fixed.

Total value of work also falls as T^w falls in the second constraint. So either the prices of M and J goods go up or quantitiy of M and J falls.

Z will fall as T^z and J will fall as explained above.