Asked by Jacob Searcy on May 09, 2024
Verified
Murphy used to consume 100 units of X and 50 units of Y when the price of X was $2 and the price of Y was $4.If the price of X rose to $4 and the price of Y rose to $7, how much would Murphy's income have to rise so that he could still afford his original bundle?
A) $500
B) $750
C) $350
D) $250
E) None of the above.
Original Bundle
In economics, the combination of goods and services initially chosen or available to a consumer before considering price changes or budget constraints.
Price Rise
An increase in the cost or price of goods and services, often indicative of inflation or shifts in supply and demand dynamics.
- Calculate the increase in income needed to maintain consumption levels when prices change.
- Analyze the impact of price changes on consumer choices and budget allocation.
Verified Answer
RG
rashad greenMay 11, 2024
Final Answer :
C
Explanation :
We can use the concept of budget constraint to solve this problem. Before the price change, Murphy's total expenditure on X and Y was 100($2) + 50($4) = $300. This expenditure must remain the same after the price change. If the price of X is now $4, Murphy can only afford 100($4) = $400 worth of X. This means that Murphy now has $300 - $400 = -$100 left to spend on Y. To afford the original bundle, Murphy needs an additional $50(4-7) = $-150 for Y. Therefore, Murphy's income will need to rise by $150 - (-$100) = $250 to afford the original bundle. Thus, the answer is option C.
Another way to solve the problem is to use the concept of income elasticity of demand. The total expenditure on X and Y before the price change was $300. The income elasticity of demand for X is 0 (inelastic), which means that the quantity demanded of X does not change with income. Therefore, Murphy will still spend $200 on X after the income change. The income elasticity of demand for Y is -1/2 (elastic), which means that the quantity demanded of Y will decrease by 25% when income decreases by 50%. To maintain the same quantity demanded of Y, Murphy's income will need to increase by 25% of $100 = $25. Therefore, Murphy's income will need to rise by $200 + $25 = $225 to afford the original bundle. This calculation is slightly different from the first method because we are assuming that Murphy still consumes 50 units of Y even though his income has decreased.
Another way to solve the problem is to use the concept of income elasticity of demand. The total expenditure on X and Y before the price change was $300. The income elasticity of demand for X is 0 (inelastic), which means that the quantity demanded of X does not change with income. Therefore, Murphy will still spend $200 on X after the income change. The income elasticity of demand for Y is -1/2 (elastic), which means that the quantity demanded of Y will decrease by 25% when income decreases by 50%. To maintain the same quantity demanded of Y, Murphy's income will need to increase by 25% of $100 = $25. Therefore, Murphy's income will need to rise by $200 + $25 = $225 to afford the original bundle. This calculation is slightly different from the first method because we are assuming that Murphy still consumes 50 units of Y even though his income has decreased.
Learning Objectives
- Calculate the increase in income needed to maintain consumption levels when prices change.
- Analyze the impact of price changes on consumer choices and budget allocation.