Question 37 [ DIFFICULT] Consider two firms, both producing the same product, using the same production technology given by: a = √√√√K This production technology implies the following MRTS: ΔΥ K MRTS= ΔΧ L where K is the amount of capital used and L is the amount of labour used to produce output. It can be shown that this production technology implies the following minimised total cost function: TC = 2q√w√r where w represents the per-unit cost of labour and r represents the per-unit cost of capital. Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90 units of output. One firm (Firm 1) chooses its input combination to minimise costs of production. However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to Firm 1, how much higher are Firm 2's cost of production? a) $270 b) $67.50 c) $275 d) $135 e) $132
Question 37 [ DIFFICULT] Consider two firms, both producing the same product, using the same production technology given by: a = √√√√K This production technology implies the following MRTS: ΔΥ K MRTS= ΔΧ L where K is the amount of capital used and L is the amount of labour used to produce output. It can be shown that this production technology implies the following minimised total cost function: TC = 2q√w√r where w represents the per-unit cost of labour and r represents the per-unit cost of capital. Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90 units of output. One firm (Firm 1) chooses its input combination to minimise costs of production. However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to Firm 1, how much higher are Firm 2's cost of production? a) $270 b) $67.50 c) $275 d) $135 e) $132
Chapter22: Supply: The Costs Of Doing Business
Section: Chapter Questions
Problem 11E
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![Question 37 [ DIFFICULT]
Consider two firms, both producing the same product, using the same production technology
given by:
q = √√K
This production technology implies the following MRTS:
K
MRTS=AY
ΔΧ
L
where K is the amount of capital used and L is the amount of labour used to produce output. It
can be shown that this production technology implies the following minimised total cost
function:
TC = 2q√w√r
where w represents the per-unit cost of labour and r represents the per-unit cost of capital.
Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90
units of output. One firm (Firm 1) chooses its input combination to minimise costs of production.
However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to
Firm 1, how much higher are Firm 2's cost of production?
a) $270
b) $67.50
c) $275
d) $135
e) $132
Hint: It can be shown that the cost-minimising quantities of capital and labour (chosen by Firm
1) are K = 30 and L = 270.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86482bd7-4c15-4dcf-9c37-a459ca62a088%2Faf6db6d8-311b-43c9-8a82-0caa8c0be2e2%2Fe87wt_processed.png&w=3840&q=75)
Transcribed Image Text:Question 37 [ DIFFICULT]
Consider two firms, both producing the same product, using the same production technology
given by:
q = √√K
This production technology implies the following MRTS:
K
MRTS=AY
ΔΧ
L
where K is the amount of capital used and L is the amount of labour used to produce output. It
can be shown that this production technology implies the following minimised total cost
function:
TC = 2q√w√r
where w represents the per-unit cost of labour and r represents the per-unit cost of capital.
Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90
units of output. One firm (Firm 1) chooses its input combination to minimise costs of production.
However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to
Firm 1, how much higher are Firm 2's cost of production?
a) $270
b) $67.50
c) $275
d) $135
e) $132
Hint: It can be shown that the cost-minimising quantities of capital and labour (chosen by Firm
1) are K = 30 and L = 270.
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