A Producer Has a Production Function Given By: Y(l₁,l₂)= L₁⁰

question 81

Essay

A producer has a production function given by: y(l₁,l₂)= l₁^0.5+2l₂^0.5 where y is the level of output and l₁ and l₂
are two different types of labour that are employed. Their cost is w₁ and w₂ respectively.
a)Suppose that the input prices are both equal to w and that the output sells at price p. What is the optimal employment of two types of labour as a function of p and w?
b)Suppose that p=10, w=5. What is the optimal quantity of output produced? What is the corresponding profit?
c)What returns to scale does the production function exhibit?

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Definitions:

Z-score

A statistical measure that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean.

Finite Population Correction

An adjustment made to the standard formula for calculating sample size and variance when the sample size is a significant fraction of the total population.

Non-normal Probability Distribution

Describes a distribution of data that does not follow the normal distribution pattern, showing skewness or kurtosis different from a bell-shaped curve.

Central Limit Theorem

A fundamental statistical theory stating that, given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.