Question:

Principles of macroeconomics 2nd edition 162 2.?

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The marginal product of a worker in a light bulbs equals 30 - N bulbs per hour, where N is the total number of workers employed. Light bulbs sell for $2 each, and there are no costs to producing them other than labour costs.

a. The going hourly wage for factory workers is $20 per hour. How many workers should the fctory manager hire? What if the wage is $30 per hour?

b. Graph the factory's demand for labour.

c. Repeat Part (b) for the case in which light bulbs sell for $3 each.

d. Suppose the supply of factory workers in the town in which the light bulb factory is located is 20 workers (in other words, the labour supply curve is vertical at 20 orkers). What will be the equilibrium real wage for factory workers in the town if light bulbs sell for $2 each? If they sell for $3 each?

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  1. a)

    TR-TC=Profit

    TR-TC=Max

    (TR)'-(TC)'=0

    MR-MC=0

    MR=MC

    For wage=20

    MR=MPL*P=(30-N) * 2

    MC=W = 20

    (30-N) * 2=20

    30-N=10

    N=30-10=20

    For wage=30

    MR=(30-N) * 2

    MC= 30

    (30-N) * 2=30

    30-N=15

    N=30-15=15

    b)

    For P=2

    MR=(30-N) * 2

    MC=W

    (30-N)*2=W

    W=60-2N (Labor-demand function)

    c)

    For P=3

    MR=(30-N) * 3

    MC=W

    (30-N)*3=W

    W=90-3N (Labor-demand function)

    d)

    For P=2

    Labor-demand function: W=60-2N

    Labor-supply function N=20

    W=60-2*20=60-40=$20  per hour

    For P=3

    Labor-demand function: W=90-3N

    Labor-supply function N=20

    W=90-3*20=90-60=$30 per hour

    P.S. general labor-demand equation for this case W=(30-N)*P

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