Answer to Question #240302 in Microeconomics for Sam

Question

4. Suppose an individual has a utility function u (x1, x2) = 2*2. Present your mathmatical expressions below in the simplest form you can.

a) Derive an expression for the marginal utility of good 1, and for the marginal utility of good 2.

b) Using these, solve for an expression describing the slope of an indifference curve: MRS (11, 12).

c) Sketch indifference curves for this consumer corresponding to u = 0,10,20. (Hint: z rı = k solves for m} = 11 (21) . Solve this expression and approximate it on a graph for the three values of k.) 

Answer 1

a.

$MUX_1= \frac{∆U}{∆X_1}=$ differentiating utility function with respect to X1

•$MUX_1= (\frac{1}{2}).(X_1)^{(\frac{-1}{2})}. (X_2)^{\frac{1 }{2}}$

$MUX_2= \frac{∆U}{∆X_2}=$ differentiating utility function with respect to X2

$• MUX_2= \frac{1}2).(X1)^{\frac{1}{2}} .(X2)^{\frac{-1}{2}}$

b.$ MRS (X_1,X_2) = \frac{MUX_1}{MUX_2}$

$MRS( X_1,X_2) =\frac{{ [\frac{1}{2}.(X1)^{\frac{-1}{2}}.(X2)^{\frac{1}{2}}] }}{ {[\frac{1}{2}.(X1)^{\frac{1}{2}}.(X2)^{\frac{-1}{2}}] }}$

$*MRS(X_1,X_2) = \frac{X_2}{X_1}$

c.

The indifference curves are given below