m 4.2 Nadia likes spare ribs, R, and Fried chicken, C. Her utility function is U(R,C)=10R^2 C Her marginal utilities are 〖MU〗_R=20RC and 〖MU〗_C=10R^2 Her weekly income is $90, which she spends on only ribs and chicken. a If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show that her budget line, indifference curve, and optimal bundle, e1, in a diagram. b Suppose the price of chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e2, in a diagram. Hint: To get the right indifference curve into your picture. First, solve for the optimal R* and C* in the problem. Then substitute these values into the original utility function, V = U(R*, C*). This tells you the level of utility at the optimum. Set Utility equal to this number and solve for C in the utility function. So, solve V = 10R2C for C. This defines the indifference curve at the optimum.
m 4.2 Nadia likes spare ribs, R, and Fried chicken, C. Her utility function is U(R,C)=10R^2 C Her marginal utilities are 〖MU〗_R=20RC and 〖MU〗_C=10R^2 Her weekly income is $90, which she spends on only ribs and chicken. a If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show that her budget line, indifference curve, and optimal bundle, e1, in a diagram. b Suppose the price of chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e2, in a diagram. Hint: To get the right indifference curve into your picture. First, solve for the optimal R* and C* in the problem. Then substitute these values into the original utility function, V = U(R*, C*). This tells you the level of utility at the optimum. Set Utility equal to this number and solve for C in the utility function. So, solve V = 10R2C for C. This defines the indifference curve at the optimum.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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| Problem 4.2 | Nadia likes spare ribs, R, and Fried chicken, C. Her utility function is | |
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| Her weekly income is $90, which she spends on only ribs and chicken. | ||
| a | If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bundle? Show that her budget line, indifference curve, and optimal bundle, e1, in a diagram. | |
| b | Suppose the price of chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e2, in a diagram. | |
| Hint: | To get the right indifference curve into your picture. First, solve for the optimal R* and C* in the problem. Then substitute these values into the original utility function, V = U(R*, C*). This tells you the level of utility at the optimum. Set Utility equal to this number and solve for C in the utility function. So, solve V = 10R2C for C. This defines the indifference curve at the optimum. |
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