Crusoe Economy – Integrated Consumer-Producer Model

Question 1

What Is the Robinson Crusoe Model?

Answer 1

A model with a single agent (Crusoe) who acts as both consumer and producer, allocating time between labour and leisure, and deciding how to produce and consume.

Question 2

What roles does Crusoe play in this model?

Answer 2

Firm: Chooses labour and capital to produce output

Consumer: Chooses how much of the output to consume vs enjoy leisure

Question 3

What is the feasibility constraint in the Crusoe model?

Answer 3

Total production = total consumption

𝑌𝐹=𝑌𝐶

What the firm produces is what the consumer consumes.

Question 4

How is leisure incorporated in the Crusoe model?

Answer 4

Crusoe allocates time between labour (L) and leisure (Z). The constraint is:

L+Z=T

where T is total available time.

Question 5

What is the PPF in the Crusoe model?

Answer 5

A curve showing the maximum output Crusoe can produce at each level of labour input. It shows the trade-off between leisure and consumption.

Question 6

What defines equilibrium in the Crusoe model?

Answer 6

Tangency between indifference curve and the PPF — where the marginal rate of substitution equals the marginal rate of transformation:

MRS Z,Y=MRT Z,Y
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Question 7

How can we interpret the Crusoe model as a competitive market?

Answer 7

Crusoe “sells” labour to a firm (himself) and “buys” consumption using wage income — making it analogous to a market with wage 𝑤 and price 𝑝.

Question 8

What does Crusoe’s firm do?

Answer 8

Maximises profit:

Π=pY−wL

Chooses labour input to satisfy:
p⋅MP L=w

Question 9

What does Crusoe the consumer do?

Answer 9

Maximises utility over consumption and leisure, given the budget constraint:

pY=wL

Subject to:

Z=T−L

Question 10

What is the final equilibrium in the Crusoe model?

Answer 10

Labour choice 𝐿*such that:

MRS Z,Y =MRT -Z,Y= MP L/1
​

Question 11

What is the purpose of the Robinson Crusoe model in economics?

Answer 11

It shows how preferences and technology interact in a simple setting — integrating production, labour choice, and consumption in one coherent framework.

Question 12

What happens if you add Friday to the Crusoe economy?

Answer 12

It becomes an exchange economy with production — leads to gains from trade, division of labour, and full general equilibrium analysis (see Topic 15).