Joan can produce a maximum of 14 units of good Y and a maximum of 21 units of good X.If Y is on the vertical axis,the equation for her production possibilities curve is
A) X = 14 - 0.67Y.
B) Y = 21 - 14X.
C) Y = 14 - 0.67X.
D) Y = 14 - 1.5X.
E) X = 14 - 1.5Y.

Question

Quizplus · Accepted Answer

In order to find the equation of the production possibilities curve, we need to plot the maximum possible combinations of X and Y that Joan can produce, given her resources. 
The maximum units of Y Joan can produce is 14, and the maximum units of X she can produce is 21. 
If we put Y on the vertical axis, we can start by plotting the points (0,14) and (21,0), which represent the maximum production of Y and X respectively. 
Connecting these two points gives us a straight line, which represents the production possibilities curve.

To find the equation of this line, we need to use the slope-intercept form: Y = mx + b. 
The slope is calculated as the change in Y over the change in X, which is (14-0)/(0-21) = -0.67. 
Plugging in the slope and the Y-intercept (b=14) we get: Y = 14 - 0.67X, which is equivalent to choice C.

Joan Can Produce a Maximum of 14 Units of Good