Question

Sandy consumes only hamburgers (H) and milkshakes (M). At basket A, containing 2 hamburgers and 10 milkshakes,his MRSH,M is 8.At basket B,containing 6 hamburgers and 4 milkshakes, his MRSH,M is 1/2. Both baskets Aand Bare on the same indifference curve.Draw the indifference curve, using information about the MRSH,M to make sure that the curvature of the indifference curve is accurately depicted. 3.12. Adam likes his caffé latte prepared to contain exactly 1/4 espresso and 3/4 steamed milk by volume. On a graph with the volume of steamed milk on the horizontal axis and the volume of espresso on the vertical axis,draw two of his indifference curves,U1 and U2,with U1 > U2.

Answer 1

$$Solution$$

Since basket $A$ , containing $2$ hamburgers and $10$ milkshakes, his $MRS_{H,M}$ is $8$. At basket $B$, containing $6$ hamburgers and $4$ milkshakes, his $MRS_{H,M}$ is $\frac12$ .

At optimum, the indifferent curve is tangent to the budget line, so;

$$MRS= \frac{\rho x}{\rho y} \implies \frac{\delta x}{\delta y}=\frac{\rho x}{\rho y}$$

$MRS_{HM} \to$ At point A, the consumer has MRS of B but at point B, the MRS declines to $\frac{1}{12}$. This means Sandy was consuming more of hamburgers (H) and less of milkshake (M), and that Sandy was willing to give up more of hamburgers to get milkshake.

3.12. On a graph with the volume of steamed milk on the horizontal axis and the volume of espresso on the vertical axis,draw two of his indifference curves,U₁ and U₂,with U₁ > U₂.

Since each part of caffé latte has $0.25$ part of espresso $(ES)$ and $0.75$ part of steamed milk $(SM)$, the preferences indicate a perfect complementary relationship between espresso and steamed milk. This implies, $\frac{ES}{SM} = \frac{0.25}{0.75}\ or\ 3ES = SM.$

The utility function is given by $U = min (3ES, SM)$. We have $U_1 = 9$ so that $SM = 9$ and $ES = 3$. Similarly, $U_2 = 2$ where $SM = 2$ and $ES = 0.67$