Joe's income is $500, the price of food (F, y-axis)is $2 per unit, and the price of shelter (S, x-axis)is $100. Which of the following represents his marginal rate of transformation of food for shelter?

Question

Quizplus · Accepted Answer

The formula for the marginal rate of transformation (MRT) is the absolute value of the slope of the production possibility frontier (PPF). In this case, the PPF is a downward-sloping straight line from (0, 5) to (5, 0) on the F-S graph. The slope of this line is (change in F)/(change in S) = (-5)/(5*100) = -0.01. Therefore, the MRT of food for shelter is the absolute value of -0.01, which is 0.01 or 1/100. But we need to convert the units of the MRT to express the tradeoff between food and shelter in terms of units of food forgone for each additional unit of shelter gained. In other words, we want to know the slope of the PPF in terms of food units on the x-axis and shelter units on the y-axis. To do this, we need to multiply the slope by the ratio of the prices of food and shelter, which is 2/100 or 1/50. Therefore, the MRT of food for shelter in terms of food units is (-0.01)*(1/50) = -0.0002. This means that Joe has to give up 0.0002 units of food for each additional unit of shelter he gains. To express this as a whole number, we can invert the ratio and multiply by 100, which gives us -50. Therefore, Joe's MRT of food for shelter is -50.

Joe's Income Is $500, the Price of Food (F, Y-Axis)is