Oswald Odd consumes only goods 1 and 2.His utility function is U(x₁, x₂)=x₁ + x₂ + min{x₁, x₂}.Each of Oswald's indifference curves is A)L-shaped. B)made up of three line segments with slopes -2, -1, and -1/2. C)made up of two line segments with slopes -2 and -1/2. D)is smooth and has no kinks. E)is a diamond-shaped figure consisting of four line segments.

Question

Quizplus · Accepted Answer

Since Oswald only consumes two goods, his indifference curves will be straight lines or L-shaped curves. Furthermore, since his utility function exhibits perfect substitutes, his indifference curves will be linear with a slope that depends on the ratio of the prices of the two goods. To derive the shape of Oswald's indifference curves, we can find the marginal rate of substitution (MRS) between the two goods at any given bundle of consumption. MRS = ΔU/Δx2 ÷ ΔU/Δx1 = 1/1 This implies that Oswald is willing to substitute one unit of good 1 for one unit of good 2 at a constant rate. Therefore, each indifference curve will be a straight line with a slope equal to the ratio of the prices of the two goods. Since the prices of both goods are positive, the slope will be negative. Let's derive the slope of an indifference curve mathematically. U = F1F1F10 x₁ F1F1F1S1 + F1F1F10 x₂ F1F1F1S1 MRS = MU1/MU2 = ( F1F1F10 / F1F1F1S1 ) / ( F1F1F10 / F1F1F1S1 ) slope = - MU1/MU2 = -1 Thus, the slope of an indifference curve will be -1, and since Oswald only consumes goods 1 and 2, his indifference curves will be straight lines passing through the origin with slopes -p1/p2. Therefore, each indifference curve will be made up of two line segments with slopes F1F1F1S1F1F1F102 and F1F1F1S1F1F1F101/2. This is because the ratio of the two prices is F1F1F10/F1F1F10 = 1, and so the slopes of the indifference curves will be -1 and -1/2.

Oswald Odd Consumes Only Goods 1 and 2