Question

Chose a relationship between two variables that can be shown with a non-linear function (and is not an example from the notes). Name the functional form used, give the general formula used, sketch the graph and BRIEFLY explain your choice.

Answer 1

Cost functions can be non-linear functions. Example. Let C be the cost and Q be the number of unkts produced. Then, C= a + bQ - c(Q^2)+ d(Q^3)

We have used a Polynomial regression model.

General formula used is Y(i)=?+?1?X(i)+?2?X(i)2+?3?X3(i)

Cost curve is shaped as to show increasing returns to the variable factor initially, then constant return and finally diminishing return to the variable factor. Hence,the choice of the model.

Also, To have U-shaped Marginal and Average Cost Curve-

i)a,b and d,are each greater than zero.

ii)c<0

iii)c^2< 3*b*d