Question

Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah $10 for each finished bat. Paducah's only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below.

a. Suppose the wage is $14 per hour and Paducah’s daily fixed cost for the lathe and building is $60.

Instructions: Complete the table below. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Enter your responses as whole numbers.

Q (bats per day)	Number of employee-hours per day	Total revenue ($ per day)	Total labor cost ($ per day)	Total cost ($ per day)	Profit ($ per day)
0	0
5	1
10	2
15	4
20	7
25	11
30	16
35	22

What is the profit-maximizing quantity of bats?  bats.

b. What would be the profit-maximizing number of bats if the firm’s fixed cost were not $60 per day but only $30?

bats.

Answer 1

a)

Given Price of bat=P=$10 per unit

Wage rate=w=$14 per hour

Fixed Cost=FC=$60 per day

Q (bats per day)	Number of employee-hours per day, L	Total Revenue=TR=P*Q ($/day)	Total labor Cost=TLC=w*L ($/day)	Total Cost=TC= FC+TLC ($/day)	Profit= TR-TC	Marginal Cost per day=MC= Change in TC/Change in Q
0	0	0	0	60	-60
5	1	50	14	74	-24	2.80
10	2	100	28	88	12	2.80
15	4	150	56	116	34	5.60
20	7	200	98	158	42	8.40
25	11	250	154	214	36	11.20
30	16	300	224	284	16	14.00
35	22	350	308	368	-18	16.80

A competitive firm will increase its output as long as MC is less than or equal to P to maximize profit. We observe that MC<P for a output level of 20 bats per day. But MC>P for a output level of 25 bats per day So,

Profit maximizing quantity of bats=20 per day

b)

We know that a competitive firm makes output decisions based upon Marginal Cost. Marginal Cost depends upon the variable cost. Variable Cost is unchanged in this case. So, we can say that Marginal Cost will remain the same in this case. Hence, optimal output will be the same as in part (a). So,

Profit maximizing quantity of bats=20 per day