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In: Economics

Consider a firm who is the only employer in a small town (a labour monopsony). It...

Consider a firm who is the only employer in a small town (a labour monopsony). It faces an international price ? > 0 for each unit of output that it produces, its production function is ? = ?^? where ? > 0, and the labour supply is given by ?(?) = ? ∙ ? where ? > 0. Intuitively, the firm’s production function is concave (when ? < 1), linear (when ? = 1), or convex (when ? > 1).

a) Find the monopsonist marginal revenue product, and its marginal expenditure on labour.

b) Find the optimal number of workers that the firm hires.

c) Find the equilibrium wage in this monopsony.

d) Assume now that the labour market was perfectly competitive. Find the optimal number of workers the firm hires, and the equilibrium wage in this setting.

e) Find the deadweight loss of the monopsony (for now let’s assume ? < 1).

f) Evaluate your results in parts (a)-(e) at ? = 1 2 , at ? = 1, and ? = 2 with parameter values ? = 1, and ? = $2. How are your results affected as ? increases (that is, as the firm’s production function becomes more convex).

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Expert Solution

Rahul Sunny answered 2 years ago
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