Question

A consumer’s budget set for two goods (Xand Y) is$600⩾3X+6Y$

a.Illustrate the budget set in a diagram.

b.Does the budget set change if the prices of both goods double and theconsumer’s income also doubles? Explain.

c.Given the equation for the budget set, can you determine the prices of the two goods? The consumer’s income? Explain.

Short answer

1. Illustrated the budget set in the graphed diagram.
2. The budget set does not change even if the prices of both goods double and the consumer’s income also doubles.
3. The equation will be$3X+6Y=600$

Step-by-step solution

Illustrating the budget set:

a)

Use the following equation:

$P_{x}X+P_{y}Y=M$

Here,

$P_x$is the price ofGood X

$P_x$is the price ofGood Y

M is the Consumer’s Income.

The budget line is

$600⩾3X+6Y$

By substituting the following we will get,

$$\begin{gathered} P_{x}X+P_{y}Y=M \\ 3X+6Y=600 \end{gathered}$$

Therefore, the equation for the consumer's budget line is $10X+40Y=600$

The graph shows the maximum quantity of goods that the consumer can consume ofGood X andGood Y.

To determine the maximum affordable quantity ofGood X that can be consumed, use the following equation:

$P_x$is the price ofGood X

X is the maximum affordable quantity ofGood X

M is the Consumer’s Income

Since, the equation for the consumer's budget line is$600⩾3X+6Y$

Hence,

$\begin{array}{rcl}X& =& \frac{M}{P_x}\\ & =& \frac{600}{3}\\ & =& 200\text{units}\\ & & \end{array}$

Therefore, based on the calculation and looking at the diagram, the maximum affordable quantity ofGood X is 200 units.

To determine the maximum affordable quantity ofGood Y that can be consumed, use the following equation:

$Y=\frac{M}{P_y}$

$P_y$is the price ofGood Y

Y is the maximum affordable quantity ofGood Y

M is the Consumer’s Income

Since, the equation for the consumer's budget line is$600⩾3X+6Y$

Hence,

$\begin{array}{rcl}Y& =& \frac{M}{P_y}\\ & =& \frac{600}{6}\\ & =& 100\text{units}\\ & & \end{array}$

Therefore, based on the calculation and looking at the diagram, the maximum affordable quantity ofGood Yis 100units.

Finding the budget set if the price of both goods double and the consumer’s income also doubles 

b)

By getting through the definition of budget line we know, it is the combination of both GoodandGoodthat has a direct relationship with the consumer's income.

Therefore, if the prices of both goods double, the budget line will both shift inwards. Also, if the consumer's income doubles, both the budget line will shift outwards.We can say that; the budget set does not change if the prices of both goods double and the consumer's income also doubles.

Finding the prices of both goods and consumer’s income: 

c)

The budget line is,

$600⩾3X+6Y$

Use the following equation,

$P_{x}X+P_{y}Y=M$

Here,

$P_x$is the price ofGood X

$P_x$is the price ofGood Y

M is the Consumer’s Income.

By substituting the following we will get,

$\begin{array}{rcl}{P}_{x}X+P_{y}Y& =& M\\ 3X+6Y& =& 600\\ & & \end{array}$

Therefore,the price ofGood Xis$\$3$,the price ofGood Yis$\$6$and the Consumer’s Income is$\$600$.