Peter has a monthly income of I = $56 to spend on two goods, t-shirts (good x) and movies (good y). T-shirts cost px = $14 and movies cost py = $7. a) Write the equation of Peter's budget line and represent it graphically. Label this budget line as BLa. Look at the budget line, if Peter spends all his monthly income on t- shirts, how many t-shirts he can afford? And what is the maximum number of movies he could attend given his monthly income? [Hint: The general equation of the budget line is given by pxx+pyy = I. In this general equation, insert the given information about prices and income to find the equation of
Peter has a monthly income of I = $56 to spend on two goods, t-shirts (good x) and movies (good y). T-shirts cost px = $14 and movies cost py = $7. a) Write the equation of Peter's budget line and represent it graphically. Label this budget line as BLa. Look at the budget line, if Peter spends all his monthly income on t- shirts, how many t-shirts he can afford? And what is the maximum number of movies he could attend given his monthly income? [Hint: The general equation of the budget line is given by pxx+pyy = I. In this general equation, insert the given information about prices and income to find the equation of
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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For Part b) & c) Describe in words how Peter’s monthly consumption of the two goods is affected by this change in income & price
Transcribed Image Text:Peter has a monthly income of \( I = \$56 \) to spend on two goods, t-shirts (good \( x \)) and movies (good \( y \)). T-shirts cost \( p_x = \$14 \) and movies cost \( p_y = \$7 \).
a) **Write the equation of Peter's budget line and represent it graphically.** Label this budget line as \( BL_a \). Look at the budget line; if Peter spends all his monthly income on t-shirts, how many t-shirts can he afford? And what is the maximum number of movies he could attend given his monthly income?
*Hint: The general equation of the budget line is given by \( p_xx + p_yy = I \). In this general equation, insert the given information about prices and income to find the equation of Peter’s budget line. Next, solve for \( y \) to write the budget line in its slope-intercept form, find the vertical and horizontal intercepts, and connect them to plot line.*
b) **Suppose Peter’s income drops from \( I = \$56 \) to \( I' = \$42 \).** On the same graph from part (a), draw his new budget line (label it as \( BL_b \)) to show graphically how the location of his original budget line changes. Next, describe in words how his monthly consumption of t-shirts and movies (i.e., set of affordable bundles and maximum quantity of goods he can consume) is affected by this change in income.
c) **On a different graph, draw again Peter’s original budget line from part (a).** Suppose his monthly income remains steady at \( I = \$56 \) but movies double in price from \( p_y = \$7 \) to \( p_y' = \$14 \), while the price of t-shirts remains at \( p_x = \$14 \). Draw his new budget line (label it as \( BL_c \)) to show graphically how the location of his original budget line changes. Next, describe in words how his monthly consumption of the two goods is affected by this price change.
Expert Solution
Step 1: Define Budget Line
A budget line, also known as a budget constraint or price line, is a graphical representation used in economics to illustrate the different combinations of two goods or services that a consumer can afford, given their income and the prices of the goods.
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