Question

A consumer's income is \(£ 50\). Food costs \(£ 5\) per unit and films cost \(£ 2\) per unit. (a) Draw the budget line. Pick a point \(e\) as the chosen initial consumption bundle. (b) The price of food falls to \(£ 2.50\). Draw the new budget line. If both the goods are normal, what happens to consumption? (c) The price of films also falls to \(£ 1\). Draw the new budget line and show the chosen point \(e^{\prime \prime}\). (d) How does \(e^{\prime \prime}\) differ from \(e\) ? Why?

Short answer

Initial bundle \( e \) changes to \( e'' \) as both food and films become cheaper, leading to higher consumption.

Step-by-step solution

Understand Initial Income and Prices

The consumer's income is £50. Food costs £5 per unit, and films cost £2 per unit. This means if they spend all their money on food, they can buy 10 units (since \( \frac{50}{5} = 10 \)), and if they spend all their money on films, they can buy 25 units (since \( \frac{50}{2} = 25 \)).

Draw Initial Budget Line and Pick Point e

The budget line equation based on current prices is \( 5F + 2M = 50 \), where \( F \) is food units and \( M \) is movie units. It's a straight line from \((10, 0)\) to \((0, 25)\). Any point on this line, like \((5, 10)\), can be chosen as point \( e \).

Calculate New Budget Line after Price Drop in Food

The new price of food is £2.50. So, the budget line equation changes to \( 2.5F + 2M = 50 \). If only food is bought, \( F = 20 \) units; if only movies are bought, \( M = 25 \) units. The new budget line extends from \((20, 0)\) to \((0, 25)\).

Understand Impact of Price Change on Consumption

Since both goods are normal, after the price drop in food, the consumer might consume more of both goods due to increased purchasing power, potentially moving off point \( e \) to more food and possibly more movies.

Calculate Budget Line after falling price of movies

The price of films also falls to £1, changing the budget line to \( 2.5F + 1M = 50 \). Here, if only food is bought, \( F = 20 \); if only movies, \( M = 50 \). This gives a new line from \((20, 0)\) to \((0, 50)\).

Determine New Consumption Point e''

With further price reduction, the consumer can afford more of both goods if they are normal, potentially choosing a bundle \( e'' \) where both goods are consumed in higher amounts.

Compare e'' to e

Point \( e'' \) differs from \( e \) as prices changes increase total affordable goods. The consumer finds a new balance using more goods thanks to favorable prices. Thus, \( e'' \) represents higher consumption.

Key concepts

Budget Line

A budget line represents all possible combinations of two goods that a consumer can purchase with their given income. It's a graphical depiction of the trade-offs between two goods. In the exercise, the consumer has an income of £50. Given the initial prices (food at £5 per unit and films at £2 per unit), the budget line can be calculated using the equation \( 5F + 2M = 50 \), where \( F \) is the number of food units and \( M \) is the number of film units. This line runs from the point \((10, 0)\) to \((0, 25)\), showing the maximum number of each good that can be purchased if the consumer decided to buy only one type of product. The budget line visually outlines the limits placed on choices by income and prices. As prices change, so does the slope and position of this line, reflecting the new constraints and opportunities.

Normal Goods

Normal goods are products that people buy more of as their income increases, and less of as their income decreases. When goods are normal, a change in income or the price of a good impacts how much the consumer will want to buy.

In this exercise, when the price of food drops from £5 to £2.50, both food and films are considered normal goods. The consumer's purchasing power effectively increases as they can now buy more with the same income. This typically results in a higher quantity purchased of both types of goods, assuming no other changes in preferences or income.

The concept of normal goods is crucial in understanding consumer behavior. When prices decrease, it generally leads to increased consumption of normal goods, as more consumption bundles become affordable within the budget.

Price Effect

Price effect refers to how changes in the price of a good impact the quantity of that good demanded, holding other factors constant. A crucial distinction is observed between the substitution effect and income effect when evaluating price changes.

First, the substitution effect occurs when a good becomes cheaper relative to others, prompting consumers to buy more of the cheaper good. In our scenario, as the price of food declines from £5 to £2.50, food becomes relatively cheaper compared to films, leading consumers to substitute some film purchases with additional food, even before considering income changes.

Then, the overall price effect, which is a combination of both substitution and income effects, results in the consumer choosing a different point on a new budget line. For the consumer, they could move to a combination where both food and films are consumed in increased quantities, thanks to the improved affordability.

Income Effect

Income effect describes how a change in a consumer's purchasing power, due to a price change, affects the quantity demanded for a good. Even though the consumer's actual income doesn’t change when prices drop, it feels as though they have more money to spend because their income can buy more now.

In this exercise, when the price of food and films drops, the consumer experiences an effective increase in real income because they can afford more goods for the same economic outlay. This leads to a potential increase in the consumption of both goods if they are normal. For instance, when the price of films decreases to £1, the budget line extends, showing that up to 50 units of films can be bought now, if no food is purchased.

As both prices reduce, and considering both goods are normal, the income effect regards that more of each will be consumed, moving the consumer from point \( e \) to point \( e'' \) on the extended budget line. The income effect is an essential concept in understanding shifts in consumption caused by price changes.