Question

Plastico Inc. manufactures outdoor/deck furniture out of a proprietary plastic/fiberglass blend. It has two potential suppliers of its primary input, plastic/fiberglass pellets that are melted and extruded to produce the furniture. The two suppliers, FiberTech (FT) and Rockingham Brothers (RB), use slightly different methods to produce the pellets, so while the pellets are interchangable, it takes 1.3 times as many FiberTech pellets to produce a chair as it does Rockingham Brothers pellets.

If the pellets are priced equally, Plastico should use  

all RB pellets

. If, on the other hand, the RB pellets are twice as expensive as the FT pellets, then Plastico should use  

all FT pellets

.

Part 2   (3 points)

Suppose that Plastico's production function is given by ?=??+1.3??40y=FT+1.3RB40 , where ?y is the number of Plastico chairs produced, ??FT is the number of FiberTech pellets used, and ??RB is the number of Rockingham Brother pellets used. If the market price of each chair is $300 and pellet prices are $0.60 per pellet for FiberTech pellets and $0.64 per pellet for Rockingham Brothers pellets, then the profit-maximizing amount of each input needed to produce one chair is (round your answers to two decimal places):
     FiberTech pellets and     Rockingham Brothers pellets. Using this input mix, Plastico will earn a profit of   $   for each chair it produces.

Answer 1

1. all RB pellets; all FT pellets
(They are substitutes, so, only RB pellets will be used when they are cheaper and only FT pellets will be used when they are cheaper.)

2. 0; 30.77; 280.31
(y = (FT+1.3RB)/40
MRTS = MPFT/MPRB = (dy/dFT)/(dy/dRB) = (1/40)/(1.3/40) = 1/1.3 = 0.77
PFT/PRB = 0.6/0.64 = 0.9375
So, MRTS < price ratio. Thus, only RB will be used.
FT = 0
y = 1 = (0+1.3RB)/40
So, 1.3RB = 40
So, RB = 40/1.3 = 30.77

Profit = TR - TC = P*y - PRB*RB = (300*1) - (0.64*30.77) = 300 - 19.6928 = 280.31)