# Multiple choice Production Process Q Watch

1. Okay if you have capital and labour as perfect substitutes where:

3 units of labour equals 1 unit of capital

And the prices are:

Labour = \$1
Capital = \$4

Which of the following will the firm pick?

a- employ only capital
b- employ only labour
c- three times as much capital as labour
d- four times as much labour as capital

Why?
2. b)

call your production function: q = L + 3K. that is to produce 3 units you need 3 units of labor or 1 unit of capital. if you have Labor on the horizontal axis put a point at 3, and if capital on vertical then put a point at 1. draw a straight line. that is the contour for q = 3. Now add the isocost line. What does it cost to have 3 units of labor? It costs 3. how much capital can you get for 3 dollars? 3/4 capital. so draw a straight line from 3 to 3/4.

You see that the isocost line is shallower than the production contour. Hence you produce at the point where the two meet which is at Labour only.

Note: if say capital would have cost \$2 then you would only produce capital. In this case the iso cost line is steeper and so for the given production contour, the lowest cost is where the iso cost line (now slope 1/2) still meets the production contour is at capital only.

General rule for perfect substitutes: q = ax + by (in your case a =1 and x is labour, b is 3 and y is capital)

if w1 is price of x and w2 is price of y then

if w1/w2 < a/b (both in absolute value) you take take x only and vice versa

Hard to explain without a diagram so draw it to see it for yourself.
3. (Original post by danny111)
b)

call your production function: q = L + 3K. that is to produce 3 units you need 3 units of labor or 1 unit of capital. if you have Labor on the horizontal axis put a point at 3, and if capital on vertical then put a point at 1. draw a straight line. that is the contour for q = 3. Now add the isocost line. What does it cost to have 3 units of labor? It costs 3. how much capital can you get for 3 dollars? 3/4 capital. so draw a straight line from 3 to 3/4.

You see that the isocost line is shallower than the production contour. Hence you produce at the point where the two meet which is at Labour only.

Note: if say capital would have cost \$2 then you would only produce capital. In this case the iso cost line is steeper and so for the given production contour, the lowest cost is where the iso cost line (now slope 1/2) still meets the production contour is at capital only.

General rule for perfect substitutes: q = ax + by (in your case a =1 and x is labour, b is 3 and y is capital)

if w1 is price of x and w2 is price of y then

if w1/w2 &lt; a/b (both in absolute value) you take take x only and vice versa

Hard to explain without a diagram so draw it to see it for yourself.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 29, 2010
Today on TSR

### Degrees to get rich!

... and the ones that won't

### Women equal with Men?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

Can you help? Study Help unanswered threadsStudy Help rules and posting guidelines

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.