Production Theory Flashcards
What is the production set (P)?
The set of all feasible production plans for a given production technology
What does production function f describe?
A single output technology
What does the function f tell us?
The maximum amount of output that can be produced using input amounts x
What do isoquants depict?
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)
What is a key feature of production functions?
They are cardinal so you cannot perform a monotonic transformation on them
How do you find the marginal product from a production function?
Differentiate the whole production function with respect to the relevant good e.g df(x1,x2)/dx1
How do you find the Marginal Rate of Technical substitution (MRTS)?
- 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
What are the 3 main properties of production?
- Marginal products are positive
- Marginal products are diminishing; second derivatives of production function are less than zero
- Isoquants are convex to the origin
When are there constant returns to scale (CRS)?
f displays CRS if scaling all inputs by t>1 results in t times as much output: f(tx1,tx2)=tf(x1,x2)
When are there increasing returns to scale (IRS)?
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)
When are the decreasing returns to scale (DRS)?
f displays DRS if scaling all inputs by t>1 results in less than t times as much output: f(tx1,tx2)
What is the short-run in terms of profit maximisation?
The time period for which at least 1 factor of production is fixed
How do you solve the short-run profit maximisation problem?
- 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
What is the long-run in terms of profit maximisation?
The time period for which all factors of production are variable
How do you solve the long-run profit maximisation problem?
- 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
How can we solve the profit maximisation problem by cost minimisation?
- 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
What are the conditional factor demands?
x1 and x2 in terms of y
What is the cost function?
The final answer for profit maximising by cost minimising
How do you find total variable cost from the marginal cost curve?
Total variable cost is the area under the MC curve so you integrate the cost function
What is a key similarity between the AVC and MC curves?
They start at the same point on the y-axis
What is the main relationship between the AVC and MC curves?
AVC is falling whenever MC curve is below AVC curve and AVC is rising whenever MC curve is above it
Which solution do you choose as the optimal one if there are multiple for the PMP?
For output to be optimal it must be where the price line intersects the upward-sloping part of the MC curve
When is there a boundary solution to the PMP?
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
What is the Shut-down condition?
p
How do we derive the supply function from the cost function?
- Set price equal to marginal cost
- Rearrange to get y in terms of p and sub into the profit function
