Question

Given a consumer's utility function u(f,c) = fc^2 - 10f, an income of $100, and the price of food as $1, what is the range of prices for clothing (py) where a corner solution occurs?

a) $0 < py < $5
b) $5 < py < $10
c) $10 < py < $15
d) $15 < py < $20

Answer 1

The range of prices for clothing where a corner solution occurs is 0 < py < 0.025.

Step-by-step explanation:

To determine the range of prices for clothing (py) where a corner solution occurs, we need to find the price at which the consumer's budget constraint is tangent to the highest possible indifference curve.

The budget constraint is given by the equation 100 = 1f + py * c, where f represents the quantity of food consumed and c represents the quantity of clothing consumed. Let's assume f = 50 and py = p. Substituting these values into the budget constraint, we get 100 = 1(50) + p(50^2).

Simplifying the equation, we have 100 = 50 + 2500p. Solving for p, we get p = (100 - 50)/2500 = 0.025. Therefore, the range of prices for clothing where a corner solution occurs is 0 < py < 0.025.