[1] Delo\'s Doubles, a supplier of the Trinidadian favorite food item called dou

Question

[1] Delo's Doubles, a supplier of the Trinidadian favorite food item called doubles, one highly recommended by Prof. Gallet if you ever find yourself in Trinidad, produces doubles according to the following production function: Q 100K,LI 2 where Q is the quantity of doubles produced per day, K is the number of "doubles carts" utilized per day (which in the short run is fixed at 2), and L is the number of workers hired per day. Suppose the price of capital (Pk) is $300 (measured in Trinidadian dollars) and the price of labor (PL) is $150 (measured irn Trinidadian dollars). Note: An exponent of ½ means take the square root of the variable. Determine the total fixed cost, total variable cost, total cost, average fixed cost, average variable cost, and average total cost of producing 400, 800, and 1200 doubles per day

Explanation / Answer

It is short run production function where K=2 and L is the only variable

Q=100K^2L^(1/2)

wage rate=w=$150 and rent=r=$300

Fixed Element is r because "K" is fixed capital therefore Fixed Cost =2*300=$600

Total Variable Cost=wL=150*L

Total Cost=VC+FC=150L+600

Average Fixed Cost=FC/Q=600/(100(2)^2*(L)^1/2=1.5/sqrt(L)

Average Variable Cost=VC/Q=150*L/600*(sqrt(L)=sqrt(L)/4

Now we have Q=400,800 and 1200

When Q=400 we have sqrt(L)=Q/(100K^2)=400/(100*(2)^2=1 therefore L=1

FC=$600

VC=150*(1)=$150

TC=$750

AFC=600/400=1.5 , AVC=150/400=3/8 and ATC=1.875

When  Q=800 we have sqrt(L)=Q/(100K^2)=800/(100*(2)^2=2 therefore L=4

FC=$600

VC=150*(4)=$600

TC=$1200

AFC=600/800=0.75, AVC=600/800=0.75 and ATC=1.5

When  Q=1200 we have sqrt(L)=Q/(100K^2)=1200/(100*(2)^2=3 therefore L=9

FC=$600

VC=150*(9)=$1350

TC=$1950

AFC=600/1200=0.5, AVC=1350/1200=1.125 and ATC=1.625

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