A Producer Has Two Alternative Techniques to Produce a Unit

question 43

Essay

A producer has two alternative techniques to produce a unit of output out of labour. In the first, the production function is given by y₁(l₁)=l₁^0.5, and in the second it is given by y₂(l₂)=2l₂^0.5. The cost function c(y,w)of the producer gives the minimal expenditure required to produce a given total amount of y of the output (i.e.: y₁ +y₂
=y)at input price w.
a)Set up the cost minimisation problem and solve for the optimal choice of l₁ and l₂ as a function of the required output. Finally, derive the cost function for the producer.
b)Determine the firm supply under price- taking behaviour of the firm as a function of p and w.
c)Finally, suppose that p=10 and w=5. Determine the profit- maximising quantity produced and the associated level of profits.

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Definitions:

Sensory Memory

The shortest-term element of memory, it is the ability to retain impressions of sensory information after the original stimuli have ended.

Long-term Memory

The capacity of the brain to store, maintain, and retrieve information over long periods, which can last from hours to decades.

Procedural Memory

Refers to the type of long-term memory that is responsible for knowing how to do things, also known as motor skills.

Semantic Memory

A person’s knowledge about the world.