Consider a consumer who is choosing between cake (c) and ice-cream (i). Their utility function is given by u(xc, x¡) = xx². Initially their income is m = 10, and prices are given by pe = 2 and p = 4. а. Solve for the consumer's demand functions for c and i, and calculate their demand at the prices given above. Right before a bank holiday, the price of cake increases to $4. Calculate the consumer's demand at these new prices. b. Calculate the income and substitution effect of this price change on demand for cake. с.
Consider a consumer who is choosing between cake (c) and ice-cream (i). Their utility function is given by u(xc, x¡) = xx². Initially their income is m = 10, and prices are given by pe = 2 and p = 4. а. Solve for the consumer's demand functions for c and i, and calculate their demand at the prices given above. Right before a bank holiday, the price of cake increases to $4. Calculate the consumer's demand at these new prices. b. Calculate the income and substitution effect of this price change on demand for cake. с.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Consider a consumer who is choosing between cake (c) and ice-cream (i). Their utility
function is given by u(xc, xi) = xcx? . Initially their income is m = 10, and prices are
given by p. = 2 and p = 4.
а.
Solve for the consumer's demand functions for c and i, and calculate their
demand at the prices given above.
Right before a bank holiday, the price of cake increases to $4. Calculate the
consumer's demand at these new prices.
b.
Calculate the income and substitution effect of this price change on demand for
cake.
с.
With the aid of a diagram, explain why the weak axiom of revealed preferences
implies that the substitution effect for x, must be negative.
d.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7231bdbb-5cc1-4e37-bfcf-ee6e03afa58e%2F5190b22b-4640-4f1f-87c4-84e430045c51%2Fw9jvpqm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a consumer who is choosing between cake (c) and ice-cream (i). Their utility
function is given by u(xc, xi) = xcx? . Initially their income is m = 10, and prices are
given by p. = 2 and p = 4.
а.
Solve for the consumer's demand functions for c and i, and calculate their
demand at the prices given above.
Right before a bank holiday, the price of cake increases to $4. Calculate the
consumer's demand at these new prices.
b.
Calculate the income and substitution effect of this price change on demand for
cake.
с.
With the aid of a diagram, explain why the weak axiom of revealed preferences
implies that the substitution effect for x, must be negative.
d.
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