Question

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 ?

Answer 1

a) $U1'=X1+X2$

b)

c) $U'(x1)=MU1=\frac{X2}{8}$

$U'(x2)=MU2=\frac{X1}{8}$

$MRS=\frac{MU1}{MU2}=\frac{X2}{X1}$

e) $M=k$

$k=I^2k$

$I=1$

f) 50-days, lk-cost of production in day,we need 1000 units

$1000=50*lk$

$20=lk$