Jake spends $200 on fried chickens and Pepsi. The price of a fried chicken is $5 and Pepsi is $2.50 per bottle. With the quantity of Pepsi being measured along the vertical axis, the slope of Jake’s budget line is __ per fried chicken.
A) 0.5 of a Pepsi
B) -0.5 of a Pepsi
C) 2 Pepsi’s
D) -2 Pepsi’s
The correct answer and explanation is :
The correct answer is D) -2 Pepsi’s.
Explanation:
Jake’s budget is constrained by the amount of money he has to spend, which is \$200. He buys two goods: fried chickens and Pepsi. The price of a fried chicken is \$5, and the price of Pepsi is \$2.50 per bottle.
To understand the slope of the budget line, we first need to recall that the budget line represents all the possible combinations of the two goods that Jake can afford, given his total budget.
The budget equation is:
$$
5 \times \text{Fried Chicken} + 2.50 \times \text{Pepsi} = 200
$$
Now, let’s isolate the quantity of Pepsi (denoted as $Q_P$) in terms of the quantity of fried chicken (denoted as $Q_C$):
$$
2.50 \times Q_P = 200 – 5 \times Q_C
$$
$$
Q_P = \frac{200 – 5 \times Q_C}{2.50}
$$
$$
Q_P = 80 – 2 \times Q_C
$$
This is the equation of the budget line, where $Q_P$ is the quantity of Pepsi and $Q_C$ is the quantity of fried chickens.
The slope of the budget line is the rate at which Jake must give up Pepsi to get one more fried chicken, and it’s represented by the coefficient of $Q_C$ (the fried chicken quantity). In this case, the slope is $-2$.
This means that for every additional fried chicken Jake buys, he has to give up 2 bottles of Pepsi. Therefore, the slope of the budget line is -2 Pepsi’s, meaning Jake has to sacrifice 2 bottles of Pepsi to purchase one more fried chicken.
Intuition:
The negative sign in the slope reflects the trade-off between the two goods—if Jake spends his money on more fried chickens, he must spend less on Pepsi. Hence, the slope of the budget line is negative, showing the inverse relationship between the quantity of Pepsi and fried chickens Jake can buy.