The owner of Ohmer%u2019s Pool Service believes that the relationship between th
ID: 1177734 • Letter: T
Question
The owner of Ohmer%u2019s Pool Service believes that the relationship between the number of pools cleaned (Q) and labor input (L) is described by the following production function:
Q = 2 + 7.5 L - .5 L
2
Q is the number of pools cleaned/day.
L is the number of people employed/day
The price the firm receives is $30 for each pool cleaned (P = MR = $30 in this case or a perfectly elastic demand curve facing Ohmer%u2019s Pool Service) and the daily wage for labor (L) is $ 15/day. All other costs are assumed trivial. To find the MP
L = dQ/dL (the derivative of Q with respect to L)
a. How many units of labor (L) should be employed to maximize profit (ie optimal labor utilization)?
b. What is the profit maximizing output level Q (Use the production function)?
c. What will be the firms profit at this level of output? (Remember
%u03C0 = TR %u2013 TC)
d. Suppose a minimum wage is passed by Congress which raises the P
L to $18/hour. What will happen to the profit maximizing output level and profits?
e. Suppose the inflation increases the price of pool maintenance and price of labor both increase by 20%. How will that impact the optimal number of units of labor hired and production Q?
f. Suppose there is inflation which increases the price of pools by 50% to $45/pool but the daily price of labor only increases by 33.33% to $20/day. How would this impact the optimal number of labor units employed, production Q, and profits.
Please show your work and or any formulas you used. Will reward full points to elaborate answer. I need to reference this for future hw. Thanks!
Explanation / Answer
totql revenue=p*Q=30*(2+7.5l-0.5l2)=60+225L-15L2
TOTAL COST=15*L;
A)
PROFIT= T.R-T.C = 60+210L-15L2
TO MAXIMIZE PROFIT DIFFERENTIATE IT AND EQUATE TO ZERO WHICH GIVES 210-30L=0 THEREBY GIVING L=7.
B)
SUBSTITUTE THIS IN THE FUNCTION GIVEN FOR Q AND U GET Q=30 FOR L=7.
C)
PROFIT=30*Q-15*L WHERE Q=30 AND L=7 GIVES PROFIT=900-105=795.
D)
INSTEAD OF TAKING TOTAL COST AS 15*L WE NOW TAKE IT TO BE AS 18*L .
FOLLOWING THE SAME PROCEDURE AS IN A AND B BITS WE GET
L=6 AND Q=27
FROM THE PROFIT EQUATION :
PROFIT=60+225L-15L2-18L AND THEN TAKING ITS FIRST ORDER DERIVATIVE AND MAKING IT EQUAL TO ZERO.
E) NOW THE NEW PRICE IS 36 FOR POOL MAINTAINANCE AND 18 FOR LABOUR .
YOUR PROFIT BECOMES
PROFIT=36*(2+7.5L-0.5L2)-18*L AND THEN THE SAME PROCEDURE GIVES
L=7 AND Q=30 THAT IMPLIES THERE IS NO CHANGE.
F)
CALCULATING PROFIT USING THE ABOVE CONDITION
PROFIT=90+280L-20L2
WHICH GIVES L=7 AND Q=30;
PROFIT=45*30-20*7=1070
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