Answer to Question #222788 in Microeconomics for D12

Question

4. Consider a consumer who is choosing how many of two goods to buy: Footballs and cricket balls. The consumer has an income of $20, and the cost of a football is $4 and a cricket ball is $2.

(a) Write down the equation for the consumer’s budget constraint and graph it.

(b) The government decides that football is evil and needs to be taxed. They introduce a 50% tax on each football sold. Rewrite and re-graph the budget constraint.

(c) A new government is elected that hates all sports. They now tax both footballs and cricket balls at 50%. What does the budget constraint look like now?

Answer 1

Income=20

cost of football=4

cost of cricket ball=2

a)

budget constraint

$P_FQ_F+P_CQ_C=I\\4Q_F+2Q_C=20$

The maximum quantity of footballs the consumer can consume is $\frac{20}{4}=5$ while the maximum quantity of cricket balls the consumer can consume is $\frac{20}{2}=10$

b)

budget constraint

$P_FQ_F+P_CQ_C=I\\6Q_F+2Q_C=20$

tax on football

$\frac{50}{100}\times 4=2$

new cost on football=4+2=6

The maximum quantity of footballs the consumer can consume is $\frac{20}{6}=3.3$ while the maximum quantity of cricket balls the consumer can consume is $\frac{20}{2}=10$.

c)

budget constraint

$P_FQ_F+P_CQ_C=I\\6Q_F+3Q_C=20$

tax on football

$\frac{50}{100}\times 4=2$

new cost on football=4+2=6

tax on cricket ball

$\frac{50}{100}\times 2=1$

new cost on football=2+1=3

The maximum quantity of footballs the consumer can consume is $\frac{20}{6}=3.3$ while the maximum quantity of cricket balls the consumer can consume is $\frac{20}{3}=6.7$