Question: 3. ( 20 points ) A coal mine operates with a production function = 2 ln , where is the quantity of labour it employs

3. (20 points) A coal mine operates with a production function = 2 ln , where is the quantity of labour it employs and is total output. The firm is a price taker in the output market, where the price is currently 32. The firm is a monopsonist in the labour market, where the supply curve for labour is () = 2 + 2.

a) Find the monopsonist marginal revenue product of labour ( ), and its marginal

expenditure on labour ().

b) Find the optimal quantity of labour that the firm hires and the equilibrium wage in

this monopsony.

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

d) Explain the impact of monopsony on employment and wage, in your own words.

show work.

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