Question

A consumer lives on a diet of solely steak and potatoes. Her budget is \(\$ 30\) for every 10 days, and she must buy enough potatoes to eat at least two potatoes per day. a. A potato costs \(\$ 0.50\) and the price of a steak is \(\$ 10\). How much will the consumer purchase of each good? b. Now suppose that the price of a potato increases to S1. How much will the consumer purchase of each good? c. Now suppose that the price of a potato increases to \(\$ 1.25 .\) How much will the consumer purchase of each good? What kind of good is the potato? e. Would you expect the demand curve for potatoes to continue to follow this trend indefinitely? Why or why not?

Short answer

a. The consumer will buy 2 steaks and 20 potatoes. b. The consumer will buy 1 steak and 20 potatoes. c. The consumer will only be able to buy 20 potatoes as she can't afford a steak. d. A potato is a necessary good. e. The demand curve won't continue the same trend indefinitely as the consumer may not be able to afford the required amount of potatoes if prices continue to increase.

Step-by-step solution

a. Calculate the quantity of potatoes and steaks with the initial prices.

Given that a potato costs \$0.50, and the consumer needs at least two potatoes per day for 10 days, the minimum amount she must allocate to potatoes is \(2 \times 10 \times 0.5 = \$10\). With the remaining \$20, the consumer can afford to buy \(\frac{\$20}{\$10/steak} = 2\) steaks.

b. Calculate the quantity of potatoes and steaks when the price of a potato increases to \$1.

The minimum amount allocated to potatoes is \(2 \times 10 \times 1 = \$20\). With the remaining \$10, the consumer can afford to buy \(\frac{\$10}{\$10/steak} = 1\) steak.

c. Calculate the quantity of potatoes and steaks when the price of a potato increases to \$1.25.

The minimum amount allocated to potatoes is \(2 \times 10 \times 1.25 = \$25\). With the remaining \$5, the consumer can't afford a steak as it costs \$10.

d. Determine the kind of good a potato is.

A potato is a necessary good in this context, as the consumer must consume at least two potatoes a day regardless of the price changes. This is because the quantity demanded doesn't decrease as price increases.

e. Analyze the trend of the demand curve for potatoes.

Given that the consumer always buys two potatoes per day, the demand curve for potatoes is perfectly inelastic in respect to the price within the budget constraints. However, this will not continue indefinitely. If the price of potatoes becomes too high and surpasses what the consumer can afford within her budget, she wouldn't be able to buy the required amount of potatoes.

Key concepts

Budget Constraint

When we talk about a budget constraint, we refer to the limitations on spending based on the income or budget a consumer has. It's like a financial rulebook that dictates how much you can spend on various goods without going over budget.
In our example, the consumer has exactly $30 to spend every 10 days. She has to decide how to allocate this money between steak and potatoes, two essential goods in her diet. Her budget constraint limits her choices.
Her initial choices are driven by the prices of the goods: potatoes cost $ 0.50 each and steaks $10 each. Her minimum requirement is 20 potatoes for 10 days, costing her $10 just for potatoes. The remaining $20 she can allocate to buy steaks, about two steaks. This alignment of purchases reflects how consumers navigate their expenditures within budgetary limits.

• The constraint forces prioritization: potatoes are necessary, hence prioritized.
• Once her required potatoes are purchased, only the remaining budget can be used for steak.

Understanding budget constraints is essential as it helps consumers make rational choices that rely on their income and preferences.

Demand Curve

The demand curve represents how much of a good a consumer is willing to buy at different prices. In simple terms, it shows the relationship between price and quantity demanded.
Typically, as the price of a good goes up, the quantity demanded goes down. But in our example, the demand for potatoes is unique because the consumer's need for at least 20 potatoes over 10 days doesn't change with price variations, at least within certain limits.

Initially, with potatoes costing $0.50, she buys the exact minimum needed. When the price rises to $1 or even $1.25, she still buys the same number of potatoes, showing a steep demand curve just in this context.

• The demand curve is perfectly inelastic up to the point of budget limit. Her behavior doesn't follow classic demand curves due to the necessity of potatoes.
• However, if the price continues to rise and exceeds her total budget, she must cut back on potatoes as well.

This highlights that some goods don't always follow the typical downward slope of demand curves due to necessity or budget constraints.

Necessity Good

Necessity goods are items that consumers deem essential and continue to purchase even when their prices increase. Potatoes in our example serve as a perfect illustration of a necessity good.
Despite fluctuation in prices, the consumer maintains her purchase of 20 potatoes. This is because potatoes are a staple in her diet, essential for each day.

• Unlike luxury goods, the demand for necessity goods doesn't significantly drop with rising prices.
• They represent a basic need without which the consumer's daily life might be disrupted.

Recognizing a good as a necessity provides insight into consumer behavior, especially during price changes, as these goods are typically less sensitive to price fluctuations, up to a certain limit.

Price Elasticity

Price elasticity refers to how sensitive the quantity demanded of a good is to a change in its price. It's a crucial concept in economics as it helps us understand and quantify such changes.
In our steak and potatoes scenario, the potatoes exhibit perfect inelasticity within the given price shifts we analyzed. This is because regardless of price increases, the quantity demanded (20 potatoes) doesn't change.

However, this won't be true indefinitely. If the price reaches a level where the budget can't cover even the minimum quantity required, the demand will eventually respond.

• Inelastic demand for potatoes within certain price ranges shows limited sensitivity to price.
• Steaks, by contrast, show elastic demand as she easily cuts back on buying any steak when the budget tightens.

Understanding price elasticity is critical for predicting consumer responses in different pricing environments. It helps both consumers and producers make informed decisions regarding spending and pricing strategies.