Answer to Question #279171 in Microeconomics for penguin

Question

Jason has the following utility function: U = F²C where F is food and C is clothing. Clothing is measured on the vertical axis while food is measured on the horizontal one. 

Derive Jason's Marginal Rate of Substitution.

Does his Marginal Rate of Substitution stay constant along one of his indifference curves? Explain your answer clearly.

Answer 1

Task #279171

Solution:

Jason's utility function is given by:

$U=F^2C$

Jason Marginal Rate of substitution is obtained by dividing marginal utility of F by the marginal utility of C.

Marginal utility from F is obtained as:

$\frac{\delta U } {\delta F}= \frac {\delta F^{2}C}{\delta F}=2FC$

Marginal utility from C is obtained as:

$\frac{\delta U } {\delta C}= \frac {\delta F^{2}C}{\delta C}=F^{2}$

Now dividing marginal utility from F by Marginal utility from C gives.

$MRS=\frac {2FC}{F^{2}}=\frac {2C}{F}$

Jason Marginal rate of substitution is $\frac{2C}{F}$

No, Jason's marginal rate of substitution does not remain constant along one of his indifference curve because $MRS = \frac {2C}{F}$ which means when one more unit of F is consumed, the marginal rate of substitution will fail and does not remain constant.

The quantity of food increases while the quantity of clothes decreases. It means the numerator of MRS decreases while it's denominator increases.

Therefore MRS falls as we move downwards along a convex well behaved indifference curve.