Question

Consider a consumer who consumes only two goods, peas and beans. He has an income of \(£ 10\), the price of beans is \(20 \mathrm{p}\) per \(\mathrm{kg}(=£ 0.2)\) and the price of peas is \(40 \mathrm{p}\) per \(\mathrm{kg}(=£ 0.4)\). (a) Suppose that the consumer consumes \(30 \mathrm{~kg}\) of beans. Assuming that the consumer wants to spend all his income, how many \(\mathrm{kg}\) of peas is he going to consume? (b) Assume that the price of peas falls from \(40 \mathrm{p}\) to \(20 \mathrm{p}\). Assuming that the consumer still consumes \(30 \mathrm{~kg}\) of beans, find the new quantity of peas. (c) After the decrease in the price of peas to \(20 \mathrm{p}\), assume that the consumer is just as well off as he was in (a) if he has an income of \(£ 7.60\). However, with that income and the new price of peas he would have consumed \(20 \mathrm{~kg}\) of beans. Find the quantity of peas he would have consumed in this case. (d) Find the substitution effect on consumption of peas due to the decrease in the price of peas in \((\mathrm{c})\) (e) Find the income effect on consumption of peas due to the decrease in income \(\operatorname{in}(\mathrm{c})\)

Short answer

(a) 10 kg; (b) 20 kg; (c) 18 kg; (d) 10 kg; (e) 8 kg.

Step-by-step solution

Calculate the Cost of Beans (a)

The consumer buys 30 kg of beans at £0.2 per kg. The cost is calculated by multiplying the quantity by the price per kg: \( 30 \text{ kg} \times £0.2/\text{kg} = £6 \).

Calculate the Remaining Budget for Peas (a)

The consumer's total income is £10. After spending £6 on beans, the remaining budget for peas is £10 - £6 = £4.

Calculate the Quantity of Peas (a)

With £4 left and peas costing £0.4 per kg, the consumer can buy \( \frac{£4}{£0.4/\text{kg}} = 10 \text{ kg} \) of peas.

Recalculate for Peas with New Price (b)

With the price of peas reduced to £0.2 per kg and spending £6 on beans, the remaining budget for peas is still £4. Thus, the consumer can now buy \( \frac{£4}{£0.2/\text{kg}} = 20 \text{ kg} \) of peas.

Calculate Peas Quantity with Adjusted Income (c)

With a reduced income of £7.60 and intending to spend exactly £4 on 20 kg of beans, the consumer has £3.60 remaining. At £0.2 per kg, he can purchase \( \frac{£3.60}{£0.2/\text{kg}} = 18 \text{ kg} \) of peas.

Determine the Substitution Effect (d)

Before any income effect, the price fall allowed the consumer to increase peas consumption from 10 kg to 20 kg, a change of 10 kg. This is the substitution effect, showing how much more peas are consumed due to the peas being cheaper alone.

Determine the Income Effect (e)

Due to the spending adjustment, with the income set to £7.60 and consuming 18 kg of peas instead of 20 kg, the consumption change purely due to income is 18 kg - 10 kg = 8 kg of peas.

Key concepts

Substitution Effect

The substitution effect occurs when a change in the price of a good causes a consumer to substitute that good for another. In our exercise, when the price of peas falls from £0.4 to £0.2 per kg, peas become more attractive relative to beans, as peas are now cheaper. This price change leads the consumer to purchase more peas instead of beans, increasing their consumption of peas from 10 kg to 20 kg simply because of the price decrease. This adjustment in consumption purely due to the change in relative prices reflects the substitution effect.

Income Effect

The income effect measures how a change in consumer income, or the buying power as a result of price changes, affects consumption. In the exercise, after peas drop in price, the consumer is able to buy the same amount of goods as before but spend less money on peas, essentially freeing up extra income. With this increased real income, even when total income fell to £7.60, the consumer could afford different combinations of peas and beans due to the lower price of peas. The increase from 10 kg to 18 kg of peas shows how consumption changes due to increased purchasing power, demonstrating the income effect apart from relative price benefits.

Budget Constraint

A budget constraint represents all possible combinations of goods that a consumer can purchase with their income at given prices. In this exercise, the consumer's budget constraint defines how much they can spend on peas and beans with a total income of £10 initially. When prices change, or income adjusts, the budget constraint shifts, allowing for different consumption choices. When peas cost £0.4, the consumer could afford 10 kg of peas after buying beans. However, with peas at £0.2 per kg and even after the income drops to £7.60, the consumer is able to purchase 18 kg, illustrating how their budget constraint could stretch with price changes or income adjustments.

Price Elasticity

Price elasticity reveals how sensitive the quantity demanded of a good is to a change in its price. In our example, the price of peas falls by half, from £0.4 to £0.2 per kg, and the quantity demanded doubles from 10 kg to 20 kg. This significant change indicates a high elasticity, showing consumers are very responsive to price changes. Such elasticity can directly influence how spending decisions align with preferences and budget constraints, adapting significantly with even a small change in pricing. Understanding elasticity helps predict shifts in consumption, ensuring effective resource allocation for both consumers and policy applications.