Question

Hank’s Hamburger Palace operates in the perfectly competitive hamburger business. The fixed costs for the business are $50. Each hamburger sells for $1 and the cost of hiring a new worker is $30. The first two columns in the table below show how many workers it takes to produce a certain number of hamburgers.

  

Quantity of Labor	Quantity of Output	Fixed Costs	Variable Cost	Total Cost	Marginal Cost	Average Cost
1	40	50	30	80		80
2	75	50	60	110	30	55
3	105	50	90	140	30	46.66667
4	130	50	120	170	30	42.5
5	150	50	150	200	30	40

a. Use the derived demand approach to calculate what quantity of labor will be hired.

  

b. Calculate the marginal revenue product and determine what quantity of labor to hire.

  

c. Do your answers match from parts b and c? Would you expect the answers to match?

Answer 1

The Price of a hamburger = P =$1

Wage rate = w = $30 per worker

Fixed cost = $50

a.

Under the derived demand approach, the quantity of labor will be hired would be determined as the units of labor that would be required to produce and supply the profit-maximizing output.

Under profit-maximization, MR = MC

TR = PQ

MR(Q2) = (TR(Q2) - TR(Q1)/(Q2-Q1)

Quantity of Labor (L)	Quantity of Output (TP)	Fixed Costs (FC)	Variable Cost (VC)	Total Cost (TC)	Marginal Cost (MC)	Average Cost (AC)	TR = P*Q	MR
1	40	50	30	80		80	40	40
2	75	50	60	110	30	55	75	35
3	105	50	90	140	30	46.66667	105	30
4	130	50	120	170	30	42.5	130	25
5	150	50	150	200	30	40	150	20

Thus, the profit-maximizing level of output = 105

To produce 105 units, the number of labor hired by the firm is 3

b.

The demand curve of the labor is given by:

Marginal Revenue Product of labor = Marginal Physical Product of Labor * Price of the hamburger

MRPL = MPPL * P

MPPL at L2 units of labor = (TP(L2) - TP(L1))/(L2-L1)

Quantity of Labor (L)	Quantity of Output (TP)	Fixed Costs (FC)	Variable Cost (VC)	Total Cost (TC)	Marginal Cost (MC)	Average Cost (AC)	Marginal Physical Product of the Labor (MPPL)	Marginal Revenue Product of the Labor (MRPL)
1	40	50	30	80		80	40	40
2	75	50	60	110	30	55	35	35
3	105	50	90	140	30	46.66667	30	30
4	130	50	120	170	30	42.5	25	25
5	150	50	150	200	30	40	20	20

Thus, the demand curve of labor is:

Quantity of Labor (L)	Marginal Revenue Product of the Labor (MRPL)
1	40
2	35
3	30
4	25
5	20

Thus, at the wage rate of $30, the equilibrium in the labor market is given by w = MRPL

Thus, the firm would hire 3 units of labor.

c.

Yes, the answers match from part a and b. Yes, the answer was expected.

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