1) Prince can consume 2 goods X1 and X2 at a price p1 and p2 respectively .Princes preferences are represented by the following utility function U1 (X1,X2) =X1 ,X2 and has an income of M .
a ) Derive Princes Marshallian demand functions for the 2 goods .
b) What are the Marshallian demand curves for the 2 goods if Princes utility changes to U2(X1, X2)=1/8(X1,X2).
c) Derive an expression for the marginal rate of substitution (MRS) between X1 and X2 for U2(X1 ,X2)=1/8(X1 ,X2).
d) Suppose a production function is given by f(k,l) =l ² k ,the price of capital is $10 and of labour $15.What combination of labour and capital minimises the cost of producing any given output
e) The production function of a given product is given by q=50kl. If the price of capital is $120 per day and the price of labour is $30 per day, what is the minimum cost of producing 1000 units of output
1
Expert's answer
2020-07-15T12:58:39-0400
a) "U1'=X1+X2"
b)
c) "U'(x1)=MU1=\\frac{X2}{8}"
"U'(x2)=MU2=\\frac{X1}{8}"
"MRS=\\frac{MU1}{MU2}=\\frac{X2}{X1}"
d) "M=k"
"k=I^2k"
"I=1"
e)50-days, lk-cost of production in day,we need 1000 units
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