Question

Restaurant meals and housing (measured in the number of rooms) are the only two goods that Neha buys. She has income of \(\$ 1,000 .\) Initially, she buys a consumption bundle such that she spends exactly half her income on restaurant meals and the other half of her income on housing. Then her income increases by \(50 \%\), but the price of restaurant meals increases by \(100 \%\) (it doubles). The price of housing remains the same. After these changes, if she wanted to, could Neha still buy the same consumption bundle as before?

Short answer

Answer: Yes, Neha can still buy the same consumption bundle after the given changes.

Step-by-step solution

Calculate the initial consumption

Neha spends half her income on restaurant meals and the other half on housing. With an initial income of \(1,000, she spends \)500 on restaurant meals and $500 on housing.

Calculate the new income

Neha's income increases by \(50\%\). So, her new income is \(1,000 \times (1 + 0.5) = \$1,500\).

Calculate the new price of restaurant meals

The price of restaurant meals increases by \(100\%\). Let the initial price of restaurant meals be \(P_r\), then the new price is \(2P_r\).

Calculate the new amount spent on restaurant meals

With the new price of restaurant meals, we need to find out how much Neha can spend on restaurant meals with her new income. Initially, she spent \(500\) on restaurant meals, so we need to see how many units of meals she can buy now.Visualizing the equation, we can write it like this: $$500 = xP_r$$ where, x is the number of restaurant meals purchased initially. Now, we'll find out the cost of these meals with the new price: $$New\,Cost\,of\,Restaurant\,Meals = x(2P_r)$$

Check if Neha can still buy the same consumption bundle

To find out if Neha can still buy the same consumption bundle, her new income should be able to cover the new cost of restaurant meals and the unchanged cost of housing. $$1,500 \ge x(2P_r) + 500$$ Since the cost of housing remains the same, Neha would just need enough income to cover the new cost of restaurant meals. If the inequality is true, Neha would be able to still buy the same consumption bundle. Solving the inequality using our initial equation (from Step 1): $$1,500 \ge x(2P_r) + 500$$ $$1,500 \ge x(2(\frac{500}{x})) + 500$$ $$1,500 \ge 1,000 + 500$$ $$1,500 \ge 1,500$$ The inequality holds true, which means that Neha can still buy the same consumption bundle as before.

Key concepts

Income Effect

The income effect helps us understand how a change in a consumer's income impacts their purchasing behavior and choice of goods. In Neha's case, her income increased from $1,000 to $1,500, which is a 50% rise. The increase in income means that Neha has more money available to spend on goods without necessarily having to change her consumption habits.
If all else remains constant, a higher income would usually allow a consumer like Neha to purchase more of both goods in her consumption bundle, possibly leading her to upgrade her lifestyle.

• The increase in income leads to greater purchasing power, which theoretically should allow Neha to consume more restaurant meals and housing rooms.
• However, despite the higher income, Neha's actual purchasing ability also depends on how prices of goods change concurrently, which we will explore next.

Understanding how income influences the consumer's ability to buy goods offers insight into broader economic behaviors related to income elasticity of demand.

Price Effect

The price effect describes how changes in the price of a good impact a consumer’s purchasing ability and choices. In Neha's scenario, after her income rose, the price of restaurant meals doubled, meaning that each meal now costs twice as much as before.
This significant price change affects Neha's consumption behavior, as it alters the affordability of one of the goods in her bundle, independently of her income change.

• The direct consequence of this price change is that Neha needs to reconsider how much of her income can be allocated to restaurant meals if she wants to keep her spending in equilibrium.
• It's essential to analyze whether the increase in her income compensates for the increased cost of dining out, which in this case, it does. In mathematical terms, though the price doubled, Neha's income increase covers the additional cost.

By understanding the price effect, one can observe how fluctuations in prices impact consumer choices in terms of buying patterns and overall welfare.

Budget Constraint

A budget constraint represents the combinations of goods a consumer can purchase given their income and the prices of those goods. For Neha, her initial budget constraint with a $1,000 income would have clearly delineated how much she could spend on restaurant meals versus housing.
After her income increased to $1,500 and the price of restaurant meals doubled, the budget constraint line shifted, reflecting both her new income and the new prices.

• To remain on her original consumption bundle while her income changed, Neha had to check if the increased income and new prices still intersect at the original point of purchase.
• Theoretically and through calculation, Neha's new income allows her to maintain her previous consumption levels, as the changed budget still meets the costs." Thus, the budget constraint dynamics are crucial in understanding the choices available.

A budget constraint acts as a limiting factor and helps visualize the trade-offs a consumer must make between two goods when their financial landscape or market prices evolve.