Question

Alfred, King of the Saxons, has a finite feudal land to cultivate. At his disposal he has two types of input: peasants (L) and hoes (K). Peasants and hoes are perfect complements, because a peasant without a tool cannot cultivate the land, and a hoe without a peasant using it is useless. Consider the number of acres of cultivated land as output y. The production function is y = (min{L,K})^⅔.

1. If King Alfred has 64 peasants and 64 hoes, how many acres can he cultivate?

2. Starting at the production point of part a, what is the marginal product of adding an additional hoe?

3. Suppose that King Alfred has 64 peasants and 65 hoes. What is the marginal product of adding an additional peasant?

4. Back to the production point of part a. What is the Technical Rate of Substitution (TRS) between peasants and hoes?

e. King Alfred annexes Essex, Sussex, Mercia and the county of Kent. Now he has eight times more peasants (512) and hoes (512). Does his production increase eight-fold, less than eight-fold, more than eight-fold?

Answer 1

A) The production function shows thaat inputs are perfect compliment,means they always use in fixed proportion to produce.

Here proportion is K=L

Q=min{ 64,64}^2/3=64^2/3=16

B) additional hoe will not produce additional unit until additional peasant come.so marginal product is zero.

C)additional peasant will not produce additional unit until additional hoe come.so marginal product is zero.

D)TRS ,shows the unit substitue of a input to increase the other input units to produce same level of production.

As both input is use in fixed proportion,so hiring additional unit of hoes will not Increase Production,so there will be no need to substitue peasant to maintain production level at same level,so TRS will be zero.