Problem 1: Isoquant, Isocost Cost Minimizing Approach to Factor Selection:
Suppose Mr Once-ler has a thneeds company called “Thneed Inc.”. Thneeds are soft fluffy things of
questionable utility that people think they need. They are made from the soft tufts of the truffula trees.
Suppose he has received an order to make 10,000 thneeds. Let Q represent the quantity of these thneeds
produced per month.
Suppose there are two factor inputs, L (labour) and truffula trees (K) where in this case, K is referred to
as “natural capital”. Mr Once-ler needs to decide how human hours of labour (L) [in hours/month] and
truffala trees (K) [in trees/month] to hire or cut down respectively to make 10,000 thneeds over a 1 month
period.
Let the production function be:.
� = �(�, �) = 100 ∗ �!/# ∗ �$/#. [1]
A is the Technical Factor Productivity term (TFP) and is equal to 100.
The marginal product of labour and capital are respectively:
��%(�, �) = 25 ∗ 0
&
%
1
$/#
[2]
and
��&(�, �) = 75 ∗ 0
%
&1
!/#
[3]
a) Find the equation of the isoquant for the production of Q = 10,000 thneeds. Rearrange to get K as a function of L.
b) Plot and label this isoquant on graph paper labeled as Fig. 1.
c) Find the marginal rate of technical substitution (MRTSL,K) as a function of L and K. This can be thought of as the marginal benefit of hiring an additional labour hour in terms of saved truffala trees while keeping output constant.
d) Suppose that the hourly rate of labour is w = $20/hour and the opportunity cost of cutting down a truffala tree is r = $40/tree. Write down a general equation of an isocost where TC represents total costs per hour due to these factor inputs. Fill in values of the K and L intercepts for a variety of total costs shown in Table 2 and then plot and label them on Fig. 1 along with your isoquant.