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)=⅛(X¹ ,X²).
c)Derive an expression for the marginal rate of substitution (MRS) between X¹ and X² for U²(X¹ ,X²)=⅛(X¹ ,X²).
e) suppose a production function is given by f(k,l) =l²k ,the price of capital is $10 and of labour $15.What combination of labour and capital minimises the cost of producing any given output
f) 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 ?
a) "U1'=X1+X2\ufeff"
b)
c) "U'(x1)=MU1=\\frac{X2}{8}"
"U'(x2)=MU2=\\frac{X1}{8}"
"MRS=\\frac{MU1}{MU2}=\\frac{X2}{X1}"
e) "M=k"
"k=I^2k"
"I=1"
f) 50-days, lk-cost of production in day,we need 1000 units
"1000=50*lk"
"20=lk"
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