Question

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

Answer 1

a) $U1'=X1+X2$

b)

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

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

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

d) $M=k$

$k=I^2k$

$I=1$

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

$1000=50lk$

$20=lk$