ProfitUniversityproducesstudentcredithours(y)withtwoinputs:Professors? hoursofwork(X1)andTAs?hoursofwork(X2)accordingtotheproductionfunction: f(X1,X2)= 10X 1 .5 X 2 .25...

ProfitUniversityproducesstudentcredithours(y)withtwoinputs:Professors?
hoursofwork(X1)andTAs?hoursofwork(X2)accordingtotheproductionfunction:
f(X1,X2)= 10X₁
^.5X₂
^.25

Bothinputsarevariable.Supposeprofessorsarepaid$80perhourandTAs
arepaid$2.5perhour.Profitsreceive$40percredithour.

1.(CostMinimization)
a) whataretheexpressionsforthemarginalproductofeachofthetwoinputsin producing credit hours?

b)Whatis the expression for the marginal rate of technical substitution of professor's
hours by TA's hours?Interpret MRTS in words.
c) Suppose that profits needs to produce 2000 credit hours this quarter. What
is the expression for the respectivei soquant?DrawthisIsoquant.
d) what is the minimum cost combination of inputs required to produce 2000 credit
hours?
e)show that given these input prices ,the cost function for profit's isC(Y)= 120(Y/20)^4/3

2.(Profitmaximizationgivencostfunction)suppose that profits faces the cost

function derived in part3(e)
a)compute the expression for profit's marginal cost,average cost as a function of Y.
b)what is the expression for profits as a function of prices and output?
c)compute the value of output that will maximize Profit's profit. what is the
maximum profit that Profits can earn?