Question

Researchers at the University of California, Davis estimate that taking walks in forests improves human health by reducing blood pressure and anxiety. They conduct research on those who take walks in forests and those that do not and find that marginal benefit (v) = 20 – 4*Q, where v is the value of an additional walk and Q is the number of walks. For simplicity, suppose we can convert v to monetary units like dollars.

a. For each additional walk, by how much does the marginal benefit decline?

b. What is the maximum v possible to walkers?

c. After how many walks are people worn out and V is driven to 0?

d. At what level of v is Q at a maximum, assuming V cannot be less than 0?

e. At what level of v is Q at a minimum?

f. Suppose Q = 2, 3 and 4, what are the predicted values of v?

g. Suppose v = 4, 8 and 12, what are the predicted values of Q?

Answer 1

a.

The marginal benefit declines by 4 for every walk taken.

b.

The maximum v possible to walkers is 50.

If we equate marginal benefit (MB) equal to zero we get Q as 5. At Q = 5, the total value of v is at its highest of 50. The Total Benefit (v) function is the integration of the MB function  .

c.

After 5 walks people are worn out and the marginal benefit is equal to zero.

d.

The benefits from walking in the forest is the dependent variable in this model, therefore it cannot predict the value of the quantity of walks Q. However at value of (v) = 0, one of the values of Q (since total benefit is a quadratic function) the highest value of Q is 10. But if the inverse were asked, at which levels of Q is (v) maximised then the answer is at Q = 5, (v) maximised at 50. But the value at which Q will be maximised is the (v) = - infinity.