Question

The table below provides the production function for Danny’s Deliveries, a bicycle delivery service in an urban area. Danny’s operates in a perfectly competitive market and charges $20per delivery. Employees are equally proficient at riding a bicycle, and Danny is able to hire as many constant-quality (equally productive) delivery persons at the going market wage rate as he wants. Assume labor is the only variable input,Danny has fixed costs of $50per day, and Danny’s goal is to maximize profit.

TC TVC+TFC Profit MPL = AQ/AL MRPL VMPL TVC- Lx W #workers | Output/Day 20 30 4 40 38 Complete the table and fill in the blanks for numbers 1 -3 below assuming that the wage rate is $80 per day worker. Diminishing returns to labor set in when Danny hires the 2 Danny is hiring workers in a labor market that is 3.Applying the profit-maximizing hiring rule, Danny hires Fill in the blanks for numbers 4 - 6 below assuming that the wage rate increases to $100 per day 4.According to the profit-maximizing hiring rule, Danny should hire workers. workers his TC = and his profit- Danny's TR workers If Danny has fixed costs of $75 instead of S50 per day, he should hire

Answer 1

L	Q	MPL	MRPL=20xMPL	TR = 20xQ	TVC=80xL	TFC	TC	PROFIT=TR-TC
0	0			0	0	50	50	-50
1	8	8	160	160	80	50	130	30
2	20	12	240	400	160	50	210	190
3	30	10	200	600	240	50	290	310
4	36	6	120	720	320	50	370	350
5	40	4	80	800	400	50	450	350
6	38	-2	-40	760	480	50	530	230

(1) Diminishing returns starts when MPL starts falling when one more worker is hired, i.e. with 3 workers being hired.

(2) Danny is hiring in labor market which is perfectly competitive (since wage rate is constant at $80).

(3) Profit is maximized when MRPL = Wage rate = $80, which holds true when 5 workers are hired.

When w = $100,

L	Q	MPL	MRPL=20xMPL	TR = 20xQ	TVC=100xL	TFC	TC	PROFIT=TR-TC
0	0			0	0	50	50	-50
1	8	8	160	160	100	50	150	10
2	20	12	240	400	200	50	250	150
3	30	10	200	600	300	50	350	250
4	36	6	120	720	400	50	450	270
5	40	4	80	800	500	50	550	250
6	38	-2	-40	760	600	50	650	110

(4) Profit is maximized when MRPL = Wage rate = $100, or if equality does not hold, MRPL must be higher than wage rate. From above table, when L = 4, MPRL = $120 > Wage rate. When L = 5, MRPL = $80 < Wage rate. Therefore 4 workers will be hired.

(5) When L = 4, TR = $720, TC = $450, Profit = $270.

(6) Since hiring rule is MRPL = Wage rate, and neither MRPL nor wage rate is determined by fixed cost, an increase in fixed cost will not change hiring decisions and 4 workers will be hired.