Assume Home produces only X-ray machines (X) and Yurts (Y). Both X and Y are produced with labor and one other fixed input specific to that product (radium for X-ray machines, sheep’s wool for Yurts). As a result, marginal products are diminishing, as shown in this table below:

L X	MPL X	L Y	MPL Y
1	100	1	20
2	90	2	17
3	80	3	14
4	70	4	11
5	60	5	8
6	50	6	5

For both X and Y, calculate the total produced for each amount of labor by adding up the marginal products.

Assume Home has 6 workers who are fully employed producing either X or Y. Using the four-quadrant diagram, draw the PPF for Home (to scale, with X on the horizontal axis), and calculate the slope between each two points on the PPF. Show that the slope is always equal to the ratio of the marginal products between two production points.

Assume each X sells for $35, and each Y sells for $200. What point of the PPF will be tangent to the slope of -P _X /P _Y (a.k.a., the CPF)? What allocation of labor will lead to the highest output (GDP = P _X Q _X + P _Y Q _Y ) for Home? What is the wage rate that results from this optimum for each sector?

Using the marginal products and prices above, carefully draw a labor allocation graph for L _X and L _Y (with W _X on the left and W _Y on the right), and show the equilibrium allocation. Calculate the gross profits for each sector ( =P _i Q _i - WL _i ), as well as the total wages received by labor.

Now, suppose that the Home Country opens up to trade, and P _Y falls to $105. What is the new equilibrium wage rate? What happens to the gross profits in each sector?

Answer rating: 100% (QA)

The total product of X and Y is given in the table below in the column as TPX and TPY LX MPX TPX ... View the full answer