Question

A consumer spends all of her income​(Y) on two goods Z and B.The price of good B ​(PB​) is $6. The Marginal Rate of Transformation MRT is equal to −2. That is 2 units of good B can be traded for 1 unit of good Z.This consumer is able to buy 18 units of good Z and 0 units of good B with​ his/her income. What is this​ consumer's level of​ income?

The​ consumer's income is ​$ ( )​(round your answer to the nearest ​penny).

Answer 1

The consumer's level of income is calculated by multiplying the price of good Z by the number of units purchased. Given the MRT of -2 and the price of good B, the price of good Z is twice that of good B. With 18 units of good Z purchased at $12 each, the income is $216.

Step-by-step explanation:

Given that the price of good B (PB) is $6, and the client is able to purchase 18 units of good Z without purchasing any units of good B, we must find the implicit price of good Z. Considering the Marginal Rate of Transformation (MRT) is -2, two units of good B can be exchanged for one unit of good Z. This means that the price of good Z (PZ) can be calculated as two times the price of good B, which is $12.

Since the consumer purchases 18 units of good Z, we can calculate the consumer's income (Y) by multiplying the quantity of good Z by the price of good Z (PZ), which gives us Y = 18 units * $12/unit. Therefore, the consumer's income is $216.

Answer 2

The consumer's income is $216.

Step-by-step explanation:

A consumer consumes two goods Z and B.

The price of good B is $6.

The consumer is consuming 18 units of good Z and 0 units of good B.

The marginal rate of transformation is the ratio of the price of two goods.

The marginal rate of transformation is -2.

MRT =
`(Pz)/(Pb)`

2 =
`(Pz)/(6)`

Pz = 12

The budget constraint will be

=
`12\ *\ 18\ +\ 6\ *\ 0`\

= $216