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AAE 320 Problem Set #2 Name:____________________________________ Due October 5, 2016

 

1) You are a beef farmer deciding on your ration for steers on your feedlot. You used your

 

records and data from a local consultant to estimate the amount of hay and grain to put 500

 

pounds of gain on your cattle. You have constructed the table below. Fill in the table below and

 

answer the following questions.

 

Hay

 

(lbs/animal)

 

1,330 Grain

 

(lbs/animal)

 

810 1,120 865 990 930 865 1,020 780 1,090 700 1,185 650 1,280 Marginal Rate of

 

Technical Substitution Price Ratio a) If the price of grain is $250.00/ton and the price of hay is $152.50/ton, what is the

 

economically optimal amount of grain and hay to feed to your cattle? (You may need to

 

interpolate between entries on the table.) b) How does your answer change if the price of grain falls to $200.00/ton and the price of hay

 

increases to $165/ton? (You may need to interpolate between entries on the table.) 1 2) You have a summer internship with a swine company. From their scientists, you obtain the

 

following production function for the final weight for feeder pigs bought to feed and sell as hogs:

 

W = ? 900 + 7C + 8S ? 0.06C2 ? 0.07S2 + 0.08CS,

 

where W is each hog?s final weight in pounds, C is pounds of ground corn consumed and S

 

pounds of soybean meal consumed. Answer the following questions:

 

a) If the price of hogs is $70/cwt (hundredweight), the price of ground corn is $120/ton, and the

 

price of soybean meal is $320/ton, what are each of these prices in $ per pound? b) How much ground corn and soybean meal is it economically optimal to feed the feeder pigs?

 

First write out the profit equation using the prices in $ per pound. Second, take the two first

 

derivatives and set them equal to zero. Third, solve these two equations for S and C. Fourth,

 

check the second order conditions. 2 c) When feeding these levels of S and C, what is the final weight of the hogs? d) When feeding these levels, what is the net return per feeder pig? Assume net return is pW ?

 

rcC ? rsS ? 120, where p, rc and rs are the prices of hogs, ground corn and soybean meal in $

 

per pound and $120 is all other costs as $ per pig. 3

 







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