Suppose a consumer has an income $\mathrm { I } = \$ 50$ which he/she spends on pizza and tacos per month. The price of pizza is $\$ 10$ and the price of tacos is $\$ 5$. Letting $Z =$ the quantity of pizza per months and $T =$ the number of tacos per month, the equation for the budget line is best represented by
A) $10 = 10 Z + 5 T$
B) $1000 = 20 Z + 10 T$
C) $50 = 10 Z + 5 T$
D) $1000 = A + B$

Question

Quizplus · Accepted Answer

The budget line equation represents all possible combinations of pizza and tacos that the consumer can buy with his/her given income. In other words, it shows the combinations of pizza and tacos which lie on the budget line. The equation for the budget line is given by:

Income = Price of Pizza x Quantity of Pizza + Price of Tacos x Quantity of Tacos

Substituting the given values, we get:

$\mathrm { I } = \$ 50$
Price of pizza = $\$ 10$
Price of tacos = $\$ 5$

Budget line equation = $50 = 10Z + 5T$

Therefore, option C is the correct choice. The budget line represents all possible combinations of pizza and tacos that a consumer can buy with his/her given income. The equation of the budget line is: 
$$I = P_PZ + P_TT$$
where $P_P$ is the price of pizza, $P_T$ is the price of tacos, $Z$ is the quantity of pizza, and $T$ is the quantity of tacos. 
Substituting the given values:
$$\$50 = \$10Z + \$5T$$
Dividing by 5, we get:
$$\$10 = 2Z + T$$
or
$$T = \$10 - 2Z$$
This is the equation of the budget line. It shows that for every unit of pizza a consumer buys, he can buy two units of tacos, given his income and the prices of the two goods. 
Therefore, the best choice(s) depend on the consumer's preferences and utility function. If the consumer values pizza and tacos equally, he will choose the point on the budget line where the slope is -2, i.e., where he buys twice as many tacos as pizza. This corresponds to point (5,10) on the budget line. If he values one good more than the other, he will choose a point on the budget line that maximizes his utility subject to his budget constraint.

Suppose a Consumer Has an Income I=$50\mathrm { I } = \$ 50I=$50

Suppose a Consumer Has an Income $\mathrm { I } = \$ 50$