Illustrate the effect of capital formation by comparing the production possibility curves, at the present time and ten years in the future, for two economies, one with a high and the other with a low rate of capital formation.

Capital formation is the process of increasing the productive capacity of an economy by adding to its capital stock, such as through investments in physical capital (e.g., machinery, infrastructure) and human capital (e.g., education, training). A higher rate of capital formation means that an economy is investing more resources in increasing its productive capacity. A production possibility curve (PPC) is a graphical representation of the combination of goods and services an economy can produce, given its current resources and technology. The curve shows the trade-offs between producing different goods and services. A point on the curve represents an efficient allocation of resources, while a point below the curve indicates underutilization of resources.

To illustrate the effect of capital formation, we first need to plot the current production possibility curves for both economies. Since we are given that one economy has a high rate of capital formation and the other has a low rate, we can assume that the economy with a high rate of capital formation has a greater quantity and quality of capital stock, which allows it to produce more goods and services overall. Draw two PPCs for the two economies. Label them as PPC1_high (for the economy with a high rate of capital formation) and PPC1_low (for the economy with a low rate of capital formation). The PPC1_high should be further to the right, indicating that the high capital formation economy is capable of producing more goods and services at present.

Next, we need to project the future production possibility curves for both economies after ten years. It's important to consider that the economy with a high rate of capital formation is expected to have a higher growth in productive capacity, while the economy with a low rate of capital formation will experience a slower growth. To represent this, draw two new PPCs, one for each economy, and label them as PPC2_high and PPC2_low. The PPC2_high should be further to the right, reflecting the higher growth in productive capacity for the economy with a high rate of capital formation. On the other hand, the PPC2_low should show a smaller shift to the right, indicating a slower growth in productive capacity for the economy with a low rate of capital formation.

Finally, analyze the differences between the production possibility curves for both economies at present and after ten years. The shift in the production possibility curves illustrates the effect of capital formation on the economies' productive capacity. The economy with a high rate of capital formation (PPC1_high and PPC2_high) shows a significant increase in productive capacity, reflected by the larger shift of the PPC to the right. This implies that a higher rate of capital formation can lead to more economic growth and a higher standard of living. On the other hand, the economy with a low rate of capital formation (PPC1_low and PPC2_low) exhibits a smaller increase in productive capacity, as the shift in the PPC is not as pronounced. This suggests that a low rate of capital formation can slow down economic growth and improvements in living standards. In conclusion, the comparison of the production possibility curves at present and in the future for both economies demonstrates the important role capital formation plays in fostering economic growth and development. The economy with a high rate of capital formation shows a greater increase in productive capacity compared to the economy with a low rate, illustrating the benefits of investing in capital stock.