Question

1. Angela spends all her income on cats (C) and artistie baby pictures (B). Cats cost $20 per pound a baby pictures costs $10 per sq. ft. Assume that Angela has $300 to spend and her utility function cam be represented as U(C,B) = CSB (put B on the y-axis). A) Find the MRS and the price ratio B) Find the optimal number of cats and baby pictures for Angela to purchase. What is her utility C) If the price of a cat doubles to $40, what would Angela's income have be for the optimal bundle to yield the same utility from B)? D) Find Angela's demand schedule for cats with the following prices: $10, $20, $30, and $10. E) Using the results from D), graph Angela's demand curve for cats. F) Using the utility calculated in B) with cat prices of $20, calculate the reduction in cats purchases due to the substitution effect when the price of a cat increases to $10. G) Using the utility calculated in B) with cat prices of $20, calculate the reduction in cats purchases due to the income effect when the price of a cat increases to $40.

Answer 1

(1)

U = C²B²

(a)

MUC = $\partial$ U/$\partial$C = 2CB²

MUB = $\partial$ U/$\partial$B = 2BC²

MRS = MUC/MUB = (2CB²) / (2BC²) = B/C

Price ratio = PC/PB = 20/10 = 2

(b)

Utility is maximized when MRS = Price ratio

B/C = 2

B = 2C

Plugging into budget line,

300 = 20C + 10B

30 = 2C + B

30 = 2C + 2C = 4C

C = 7.5

B = 2 x 7.5 = 15

(c)

Utility = (7.5 x 7.5) x (15 x 15) = 12,656.25

When PC = 40,

MRS = B/C = 40/10 = 4

B = 4C

Plugging into utility function,

12,656.25 = C²(4C)²

12,656.25 = 16 x C²C²

C⁴ = 12,656.25 / 16

C = (12,656.25 / 16)^1/4 = 5.3

B = 4 x 5.3 = 21.2

Required income = 40C + 10B = 40 x 5.3 + 10 x 21.2 = 212 + 212 = 424

(D)

MRS = B/C = PC/PB = PC/10

C x PC = 10B

Substituting in budget line:

300 = C x PC + 10 x B

300 = C x PC + C x PC = 2C x PC

C x PC = 150

C = 150/PC

(i) When PC = 10, C = 15

(ii) When PC = 20, C = 7.5

(iii) When PC = 30, C = 3

(iv) When PC = 40, C = 3.75

NOTE: As per Chegg Answering Policy, 1st 4 parts of the 1st question are answered.