Production Theory

Question 1

What is the production set (P)?

Answer 1

The set of all feasible production plans for a given production technology

Question 2

What does production function f describe?

Answer 2

A single output technology

Question 3

What does the function f tell us?

Answer 3

The maximum amount of output that can be produced using input amounts x

Question 4

What do isoquants depict?

Answer 4

Isoquants depict 3 variables in a 2D representation and they are the combination of inputs that produce a given level of output e.g (x1,x2;y)

Question 5

What is a key feature of production functions?

Answer 5

They are cardinal so you cannot perform a monotonic transformation on them

Question 6

How do you find the marginal product from a production function?

Answer 6

Differentiate the whole production function with respect to the relevant good e.g df(x1,x2)/dx1

Question 7

How do you find the Marginal Rate of Technical substitution (MRTS)?

Answer 7

• Fix some level of output k=f(x1,x2)
• Sub x2(x1) into the above expression: k=f(x1,x2(x1))
• Differentiate w.r.t x1
• Rearrange for -dx2/dx1 which is the answer

Question 8

What are the 3 main properties of production?

Answer 8

• Marginal products are positive
• Marginal products are diminishing; second derivatives of production function are less than zero
• Isoquants are convex to the origin

Question 9

When are there constant returns to scale (CRS)?

Answer 9

f displays CRS if scaling all inputs by t>1 results in t times as much output: f(tx1,tx2)=tf(x1,x2)

Question 10

When are there increasing returns to scale (IRS)?

Answer 10

f displays IRS if scaling all inputs by t>1 results in more than t times as much output: f(tx1,tx2)>tf(x1,x2)

Question 11

When are the decreasing returns to scale (DRS)?

Answer 11

f displays DRS if scaling all inputs by t>1 results in less than t times as much output: f(tx1,tx2)

Question 12

What is the short-run in terms of profit maximisation?

Answer 12

The time period for which at least 1 factor of production is fixed

Question 13

How do you solve the short-run profit maximisation problem?

Answer 13

• Differentiate profit with respect to x1, subbing in for y from the production function
• Check the second order condition is satisfied by making sure the second derivative is less than zero
• Equate the first derivative to zero and solve for x1, then sub into production function for y in terms of x̅2

Question 14

What is the long-run in terms of profit maximisation?

Answer 14

The time period for which all factors of production are variable

Question 15

How do you solve the long-run profit maximisation problem?

Answer 15

• Seperately differentiate profit with respect to x1 and x2 subbing in for y from the production function
• Equate each of the first derivates to zero and solve for the respective x
• Sub the optimal x’s into the production function and solve for y

Question 16

How can we solve the profit maximisation problem by cost minimisation?

Answer 16

• Rearrange production function for x1 and sub into objective function
• Differentiate w.r.t x2 then equate it to zero to solve for x2 in terms of y
• Sub in this answer into x1 then plug both x1 and x2 in terms of y into the objective function and simplify

Question 17

What are the conditional factor demands?

Answer 17

x1 and x2 in terms of y

Question 18

What is the cost function?

Answer 18

The final answer for profit maximising by cost minimising

Question 19

How do you find total variable cost from the marginal cost curve?

Answer 19

Total variable cost is the area under the MC curve so you integrate the cost function

Question 20

What is a key similarity between the AVC and MC curves?

Answer 20

They start at the same point on the y-axis

Question 21

What is the main relationship between the AVC and MC curves?

Answer 21

AVC is falling whenever MC curve is below AVC curve and AVC is rising whenever MC curve is above it

Question 22

Which solution do you choose as the optimal one if there are multiple for the PMP?

Answer 22

For output to be optimal it must be where the price line intersects the upward-sloping part of the MC curve

Question 23

When is there a boundary solution to the PMP?

Answer 23

If the firm doesn’t cover AVC (in the short-run) or AC (in the long-run) then the firm is better off producing zero output; y=0

Question 24

What is the Shut-down condition?

Answer 24

p

Question 25

How do we derive the supply function from the cost function?

Answer 25

• Set price equal to marginal cost

- Rearrange to get y in terms of p and sub into the profit function