Vasco likes spare ribs, q1, and fried chicken, q2. His utility function is U = 10q1^2 q2. His weekly income is $90, which he spends on ribs and chicken only. a. If he pays $10 for a slab of ribs and $5 for a chicken, what is his optimal consumption bundle? Show his budget line, indifference

Question

Vasco likes spare ribs, [latex]q_1[/latex], and fried chicken, [latex]q_2[/latex]. His utility function is [latex]U = 10q_{1}^{2} q_{2}[/latex]. His weekly income is $90, which he spends on ribs and chicken only.
a. If he pays $10 for a slab of ribs and $5 for a chicken, what is his optimal consumption bundle? Show his budget line, indifference curve, and optimal bundle, [latex]e_{1}[/latex], in a diagram.
b. Suppose the price of chicken doubles to $10.How does his optimal consumption of chicken and ribs change? Show his new budget line and optimal bundle, [latex]e_{2}[/latex], in your diagram.

Accepted Answer

Vasco determines his optimal bundle by equating the ratios of each good’s marginal utility to its price.

a. At the original prices, this condition is [latex]U_{1}/10 =2q_{1}q_{2} = 2q_{1}^{2}= U_{2}/5[/latex]. Thus, by dividing both sides of the middle equality by [latex]2q_{1}[/latex], we know that his optimal bundle has the property that [latex]q_{1} = q_{2}[/latex]. His budget constraint is [latex]90 = 10q_{1} + 5q_{2}[/latex]. Substituting [latex]q_{2}[/latex] for [latex]q_{1}[/latex], we find that [latex]15q_{2} = 90, or q_{2} = 6 = q_{1}[/latex].

b. At the new price, the optimum condition requires that [latex]U_{1}/10 =2q_{1}q_{2} = 2q_{1}^{2}= U_{2}/10[/latex], or [latex]2q_{2} = q_{1}[/latex].
By substituting this condition into his budget constraint, [latex]90 = 10q_{1} + 10q_{2}[/latex], and solving, we learn that [latex]q_{2} = 3[/latex] and [latex]q_{1} = 6[/latex]. Thus, as the price of chickens doubles, he cuts his consumption of chicken in half but does not change how many slabs of ribs he eats.

Question 3.4.15: Vasco likes spare ribs, q1, and fried chicken, q2. His utili...

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