In an economy where a unit of labour can produce either 1 unit of x or 4 units of y (or any linear combination of the two) and a unit of capital can produce either 4 units of x or 1 unit of y (or any linear combination of the two). There are 100 units of each means of production. Suppose now that the discovery of new production technologies allows the production of both x and y by using only one of the two means of production (without a change in their respective productivity).
1) what will be the production possibility curve?
2) What will be the opportunity cost of producing 50 units of x?
How much y can the economy produce if it only makes y. The 100 units of labor can make 400 y and the 100 units of capital can make 100 y. A total of 500. Lable 500 on the y-axis of your this PPC. Start from here. If the economy gives up 1 unit of capital (1 y) it gets 4 units of x. So, your PPC gets a downward line with a slope of -1/4. After 100 units of capital, the opportunity cost changes, you the economy has to give up labor to get x; it gives up 4 units of y to get 1 x. So, your PPC gets a downward line with a slope of -4. In the end, your PPC crosses the x and y axis at 500 each.
Use the graph to answer #2.
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To determine the opportunity cost of producing 50 units of x, you need to find the point on the production possibility curve (PPC) where the economy is producing 50 units of x.
First, locate the point on the x-axis where x = 50. Then, draw a vertical line up from this point until it intersects with the PPC.
Next, draw a horizontal line from the point of intersection to the y-axis. The value where this line intersects the y-axis represents the amount of y that the economy has to give up in order to produce 50 units of x.
By reading the y-axis value at this intersection point, you can determine the opportunity cost of producing 50 units of x in terms of y.