Question

Table 3-PEX2: A Production Function with Capital and Labor

Capital 6 346 490 600 692 775 846

(trucks) 5 316 448 548 632 705 775

4 282 400 490 564 632 692

3 245 346 423 490 548 600

2 200 282 346 400 448 490

1 141 200 245 282 316 346

15 16 17 18 19 20

Labor (workers)

4. If the output price is $5 per package, the rent for the capital is $50 per truck, and the wage of labor is $100 per worker, what is the profit if 3 trucks are rented and 20 workers are hired?

    A) pi = $3,000

    B) pi = $850

    C) pi = $1,000

    D) pi = $2,150

    E) pi = $600

5. If now the output price is $4/package, the rent is $50/truck, and the wage is $300/worker, and if 5 trucks are being rented, how many workers should be hired?

    A) 15 workers

B) 16 workers   

C) 17 workers

    D) 18 workers    

E) 19 or 20 workers

Answer 1

4) Option B

pi = $850

Calculation of profit if 3 trucks are rented and 20 workers are hired

Revenue(600 * $5)	$3000
Less: cost
Capital cost(3 * $50)	($150)
Labor cost(20 * $100)	($2000)
Profit	$850

5) Option D

18 workers  

Calculation of profit for different no of workers hired and 5 trucks are rented.

workers	15 workers	16 workers	17 workers	18 workers	19 workers	20 workers
Revenue(total output * $4)	$1264	$1792	$2192	$2528	$2820	$3100
Less: cost
Capital cost(5 * $50)	($250)	($250)	($250)	($250)	($250)	($250)
Labor cost(no of workers * $300)	($4500)	($4800	($5100)	($5400)	($5700)	($6000)
Profit/(loss)	($3486)	($3258)	($3158)	($3122)	($3130)	($3150)

Since there is loss in all level of workers hired, decision should be based on lower loss.when 18 workers a hired loss is lower.