What does Concavity imply

slope is increasing at a decreasing rate

- one agent - produce, consumes coconuts - trade off between labour and leisure (labour is a bad)

scenario one - RC as a worker consumer

maximises utility Sub production function f(L) = c Differentiate with respect to l Solve for l and then sub into f(L)=c, to find c =

scenario two - RC as a seller-firm

Maximises profit Function f(l) (product of labour) -wL, differentiate with respect to L* and get a function in terms of w - this is Labour demand Sub this function consumption function i.e f(l) - this is consumption supply

max profit is equal to consumption(w) - w.(L*(w))

Solve utiltiy maximisation problem maxC(1-L)(1-L) Where C = WL +profit(w) as found in step 2

differentiate with respect to L and set equal to zero and solve for L in terms of W - this is L** To find W equate L* = L** We should,d then sub into functions of c, l we obtained and show that they are equal

First fundamental welfare theorem

any competitive equilibrium of an economy with production is Pareto-efficient

seconf welfare theorem

Given the consumers preferences and the technologies are convex, for any given Pareto optimal allocation there are prices and an allocation of the total endowment and firm ownership shares that males the Pareto optimal allocation implementable by trading

and producing in the competitive markets

consists of all efficient points - slope is MRT, emphasing increasing opportunity cost to specialisation

comparative Advantage

Lower opportunity cost has a comparative advantage

grpahing PPF with 3 consumers

- one with Lower MRT for X will exhaust, then other producer with second lowest MRT will produce, if X is between certain values, and then final producer will produce of X is greater than the exhaustion of producer 2 and less than their production capac

smoothing out the PPF

more producers with different opportunity costs

list of non convex titles in production

- indivisibilities - workers not on a ful time contract Set up costs Externalities

Profit maximisation with PPFs

ALL AGENTS with p1/p2 GREATER than MRT, they should produce good one Agents with p1/p2 LESS than should produce good 2 Thence calculate totals of good 1 and 2 produced

profit maximisation of wot goods with smooth convex preferences

set MRT to MRS to determine the amount of ggod 1 and good 2 produced

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Production

Question	Answer
What does Concavity imply	slope is increasing at a decreasing rate
Assumptions of RC	- one agent - produce, consumes coconuts - trade off between labour and leisure (labour is a bad)
scenario one - RC as a worker consumer	maximises utility Sub production function f(L) = c Differentiate with respect to l Solve for l and then sub into f(L)=c, to find c =
scenario two - RC as a seller-firm	Maximises profit Function f(l) (product of labour) -wL, differentiate with respect to L* and get a function in terms of w - this is Labour demand Sub this function consumption function i.e f(l) - this is consumption supply
Cont	max profit is equal to consumption(w) - w.(L*(w))
Scenario three	Solve utiltiy maximisation problem maxC(1-L)(1-L) Where C = WL +profit(w) as found in step 2
cont	differentiate with respect to L and set equal to zero and solve for L in terms of W - this is L** To find W equate L* = L** We should,d then sub into functions of c, l we obtained and show that they are equal
First fundamental welfare theorem	any competitive equilibrium of an economy with production is Pareto-efficient
is convex its of technology required	no
seconf welfare theorem	Given the consumers preferences and the technologies are convex, for any given Pareto optimal allocation there are prices and an allocation of the total endowment and firm ownership shares that males the Pareto optimal allocation implementable by trading
cont	and producing in the competitive markets
PPF	consists of all efficient points - slope is MRT, emphasing increasing opportunity cost to specialisation
comparative Advantage	Lower opportunity cost has a comparative advantage
grpahing PPF with 3 consumers	- one with Lower MRT for X will exhaust, then other producer with second lowest MRT will produce, if X is between certain values, and then final producer will produce of X is greater than the exhaustion of producer 2 and less than their production capac
smoothing out the PPF	more producers with different opportunity costs
list of non convex titles in production	- indivisibilities - workers not on a ful time contract Set up costs Externalities
Profit maximisation with PPFs	ALL AGENTS with p1/p2 GREATER than MRT, they should produce good one Agents with p1/p2 LESS than should produce good 2 Thence calculate totals of good 1 and 2 produced
profit maximisation of wot goods with smooth convex preferences	set MRT to MRS to determine the amount of ggod 1 and good 2 produced

Created by: aliyah s

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