Question

A firm has production function Q(L) = aL - bL^2 + c, where a > 0, b > 0 and c > 0. The firm faces a competitive output market with price per unit equal to 2. The firm is also a monopsonist in the labor market with a supply curve w(L) = mL, where m > 0. a) Find the monopsonist's optimal level of employment, wage and cost on labor. b) Graph and calculate the deadweight loss of monopsony.

          A firm has production function Q(L) = aL - bL^2 + c, where a > 0, b > 0 and c > 0. The firm faces a competitive output market with price per unit equal to 2. The firm is also a monopsonist in the labor market with a supply curve w(L) = mL, where m > 0.
a) Find the monopsonist's optimal level of employment, wage and cost on labor.
b) Graph and calculate the deadweight loss of monopsony.

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A firm has production function Q(L) = aL - bL^2 + c, where a > 0, b > 0 and c > 0. The firm faces a competitive output market with price per unit equal to 2. The firm is also a monopsonist in the labor market with a supply curve w(L) = mL, where m > 0.
a) Find the monopsonist's optimal level of employment, wage and cost on labor.
b) Graph and calculate the deadweight loss of monopsony.

Added by Connor D.

Principles of Economics

Gregory Mankiw 8th Edition

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Solved by Expert Manasvee Singh

05/08/2023

Step 1

The MCL is the additional cost of hiring one more worker, which is the derivative of the total cost of labor (TCL) with respect to L: MCL = dTCL/dL = a - 2bL The MRPL is the additional revenue generated by hiring one more worker, which is the derivative of Show more…

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A firm has a production function Q(L) = aL - bL^2 + c, where a > 0, b > 0, and c > 0. The firm faces a competitive output market with a price per unit equal to 2. The firm is also a monopsonist in the labor market with a supply curve w(L) = mL, where m > 0. a) Find the monopsonist's optimal level of employment, wage, and cost of labor. b) Graph and calculate the deadweight loss of monopsony.

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Transcript

00:02 Hello everyone, now solving the first part we have a special scenario where there is competitive output market but monopoly is in labour market.

00:12 Now q is equals to al minus bl square plus c.

00:20 This is the production function.

00:22 Now w is equals to ml is given and p is equals to 2.

00:27 Now it is to be understood that the wage curve is the proxy for average cost curve in monopoly.

00:35 So average cost is equals to ml.

00:41 Now total as we know that total cost can be measured by multiplying the average cost by l.

00:47 So total cost will be equal to l multiplied by ml that is equals to ml square.

00:55 Talking about marginal cost, so marginal cost can be derived by differentiating the total cost by l.

01:01 So marginal cost is equals to 2 ml.

01:07 This is equation 1.

01:09 Now labour employment in monopoly happens when the marginal revenue product equals the marginal cost.

01:20 If we talk about marginal revenue product that is mrp.

01:25 So the formula for the same is the marginal product of labour multiplied by price.

01:45 Now mp can be obtained by differentiating the production function by l.

01:50 So mp is equals to a minus 2 bl.

01:55 Now p is equals to 2 is already given in the question.

02:02 So mrp is equals to a minus 2 bl multiplied by 2.

02:14 Now this will be 2 a minus 4 bl.

02:19 This is equation 2...

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