Question

Consider the optimal consumption bundle for a consumer who is choosing between two goods, x and z, which she considers perfectly substitutable for one another. In particular, her utility function from a bundle with qx units of good x and qz units of good z is given by u(qx,qz)

Answer 1

Answer: Please refer to the explanation section

Explanation:

When a consumer is choosing between two goods which are considered to be perfect substitutes , the optimal bundles choice will be the number of good x and good z that will yield maximum utility is found the ratio of Marginal utility of good x and marginal utility of good z equals the ratio of the Price of good x and the price of good z or The Marginal utility of good x per dollar must be equal to the marginal utility of good z per dollar.

Marginal Utility of good x = MUx

Marginal Utility of Good z = MUz

Utility function = U(qx,qz)

qx and qz maximises U(qx,qz) when

$\frac{MUx}{MUz}$ = $\frac{Px}{Pz}$   or  $\frac{MUx}{Px} = \frac{MUz}{Pz}$

When she receives the same marginal utility per dollar in good x and good y, utility is maximized