Lecture 4 - Production and Robinson Crusoe Econonomies Flashcards
Explain how we model a firm
- We model the firm as an entity that has some production technology that enables it to transform units of some goods ( inputs ) into units of other goods (outputs)
- Good 1 is an input Y1 < 0, as the firm is using good in order to be able to produce good 2
- Good 2 is an output Y2>0
Explain how we model a firms profit and explain the terms in the equation
- Profit ( Pie ) = P1Y1 + P2Y2
- P1Y1 < 0 and is a firms cost
- P2Y2 > 0 and is a firms revenue
What are the 5 assumptions of production sets?
- Y is non-empty. If Y was empty it would mean the firm can’t do anything else so there is no point in studying it.
- Y is closed: Diagrammatically this means it includes boundaries
- No free lunch. This means that a firm does not produce outputs without using inputs.
- Possibility of inaction. This means a firm can choose to do nothing.
- Free disposal. For any point on the productions set we can choose to predispose of one or both goods.
Explain definition 2, what makes a production set convex?
A production set is convex if for any two points when you join the two points the weighted average will also lie within the set.
Explain definition 3, ‘ the production set exhibits non increasing returns to scale’
Suggests that for any feasible output-input vector ( a point on the graph) the vector can be scaled for any point Y that lies in our production set.
Explain definition 4, ‘the production set Y exhibits non decreasing returns to scale’
This means that any point above point Y on a graph must also lie within our production set, see notes diagram for more info.
Explain definition 5, ‘the production set exhibits constant returns to scale’
This means that for any point Y in our production set it can be scaled both up and down, and therefore satisfies both increasing and decreasing returns to scale. This will only happen if the boundary of our production set is linear.
What 3 conditions are needed to ensure that there is a Walrasian equilibrium
To be in a Walrasian equilibrium we need prices P such that at p:
- Consumer allocation X has every agent choose their optimal bundle subject to their budget constraint.
- Production y has every firm maximising profits subject to their production set,
- Markets clear, meaning the amount demanded of every good equals the amount supplied of every good
At what point do we observe profit maximisation on a graph
When the production set, and the slope of the iso profit line meet
What are the 4 assumptions about firms in this economy?
- Firms are price takers. This means firms take the market price which is determined by the laws of supply and demand.
- Firms can sell as many or as few goods at they market price.
- Firms are profit maximisers
- We don’t model how economic conditions effect the market.
Describe the Robinson Crusoe model including a diagram
- Endowment Is initially made out of leisure time, but Crusoe is able to substitute lesiure time for consumption goods.
- This means we have 2 goods: Leisure time and Consumption good.
- We assume Crusoe has a quasi concave utility function, meaning convex preferences over the 2 goods.
- Also assume Crusoe has a marginal output decrease, as Crusoe works more his output decreases.
- See notes for diagram
Show the Pareto optimal point on a Crusoe diagram
See notes
Show the Walrasian equilibrium on a Crusoe diagram and explain why the budget constraint shifts out.
See notes
On a Crusoe diagram what is true when in a Walrasian equilibrium?
Slope of the production set = slope of the indifference curve
How do we find the Pareto optimal point mathematically
- dF/dK= Mu2/Mu1 = X2/X1
- Find dF/ dK and then X2 and X1 one of them should be in terms of the other
- Equal them and solve for the unknown
- Substitute the unknown into X1 and X2 to find the Pareto optimal
