Question #62976

Fence Right is a firm that supplies and installs fence. Its output follows the production function
Q = 20L – 0.5L2; where L denotes labour hours and Q the length of the fence in feet. The firm
hires labour at a wage of $25 per hour.
Hint: MRPL = MRC
a) DD has received an offer to install 200 feet of fence for a price of $480. Should DD accept
the offer?
b) What offer would be profitable if the company desires a price of $5 per foot of fence installed
(show all workings)?

Expert's answer

Q = 20L – 0.5L2; w = $25 per hour.

MRPL = MRC

a. If Q = 200 feet and P = $480, then:

20L - 0.5L^2 = 200,

L^2 - 40L + 400 = 0,

(L - 20)^2 = 0,

L = 20 workers.

Total cost is: TC = P*L = 25*20 = $500 > $480, so DD should not accept the offer.

b. MRPL = MRC and P = $5, then:

MRPL = MPL*P, MRC = w, so:

MP*P = w,

Q'*5 = 25,

20 - L = 5,

L = 15, so:

Q = 20L - 0.5L^2 = 20*15 - 0.5*15^2 = 187.5 feet offer would be profitable.

MRPL = MRC

a. If Q = 200 feet and P = $480, then:

20L - 0.5L^2 = 200,

L^2 - 40L + 400 = 0,

(L - 20)^2 = 0,

L = 20 workers.

Total cost is: TC = P*L = 25*20 = $500 > $480, so DD should not accept the offer.

b. MRPL = MRC and P = $5, then:

MRPL = MPL*P, MRC = w, so:

MP*P = w,

Q'*5 = 25,

20 - L = 5,

L = 15, so:

Q = 20L - 0.5L^2 = 20*15 - 0.5*15^2 = 187.5 feet offer would be profitable.

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