✏️ Budget Constraint Exercises

✏️ Suppose that you have a food budget of $90. Chickens cost $9 and lettuce costs $3.
Putting chicken on the vertical axis and lettuce on the horizontal, draw your budget constraint:

✏️ Suppose that the price of chicken drops to $5. How will the budget constraint move?

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If the price of chicken drops to $5, then you will be able to afford $\frac{\$90}{\$5} = 18\text{ chickens}$, so the budget line will rotate upwards .  ✅

✏️ What happens to slope if both prices double?

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Nothing. The slope of the BC will not change because Slope Of BC $=\frac{P_x}{P_y}$. If both prices double, then
Slope Of BC $= \frac{2P_x}{2P_y}$
The 2s will cancel out, and you’ll be left with $\frac{P_x}{P_y}$. This budget constraintshows prices of $5 × 2 = $10 for chicken and $6 for lettuce, along with a budget of $90.  ✅

✏️ What happens if both prices double and your income also doubles?

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Previously, $P_{Ch}=5$ and $P_L=3$. $B=90$
$\text{Y Intercept }= \frac{90}{5} = 18$
$\text{X Intercept }= \frac{90}{3} = 30$
Now, everything has doubled,
$\text{Y Intercept }= \frac{90 × 2}{5 × 2} = \frac{90}{5} = 18$
$\text{X Intercept }= \frac{90 × 2}{3 × 2} = \frac{90}{3} = 30$  ✅

✏️ Suppose that your budget constraint is the green line given in the diagram below. Your budget is $20,000. What are $P_x$ and $P_y$? For extra practice, you can repeat the exercise for the orange line.

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If B=$20K, with the green line, and the maximum number of good Y you can purchase with your budget, B is 20 Y, then

$$20 × P_Y = \$20\text{K, so }P_Y = \$1\text{K}$$

If the maximum of X you can purchase is 10, then $10 × P_X = \$20\text{K}$, so $P_X = \$2\text{K}$

With the orange line, the maximum number of good Y you can purchase is 5 Y, then

$$5 × P_Y = \$20\text{K, so }P_Y = \$4\text{K}$$

If the maximum of X you can purchase is 25, then $25 × P_X = \$20\text{K}$, so $P_X = \$800$  ✅