Output Y is produced according to Y = F(K, L), where K is the capital stock and L is the number of workers. The production function F(K, L) has constant returns to scale and diminishing marginal returns to capital and labour individually. The level of technology is assumed to be constant over time. Capital per worker is denoted by k = K/L and output per worker by y = Y/L, and the two are related according to y = f(k), where f(k) = F(k, 1) is the per-worker production function. Investment is equal to saving, which is a constant fraction s of income Y. Capital depreciates at rate δ and the number of workers grows at rate n. The change in capital per worker over time is ∆k = sf(k) − (δ + n)k. Consider a country that has reached its steady-state capital per worker. Then, in one year, the country suffers severe flooding that destroys part of its capital stock. Assume this is treated as a one-off event that is not expected to reoccur. explain what happens to income per worker in the short run and the long run.
Output Y is produced according to Y = F(K, L), where K is the capital stock and L
is the number of workers. The production function F(K, L) has constant returns to
scale and diminishing marginal returns to capital and labour individually. The level
of technology is assumed to be constant over time. Capital per worker is denoted
by k = K/L and output per worker by y = Y/L, and the two are related according to
y = f(k), where f(k) = F(k, 1) is the per-worker production function.
Investment is equal to saving, which is a constant fraction s of income Y. Capital
capital per worker over time is ∆k = sf(k) − (δ + n)k.
Consider a country that has reached its steady-state capital per worker. Then, in
one year, the country suffers severe flooding that destroys part of its capital stock.
Assume this is treated as a one-off event that is not expected to reoccur.
explain what happens to income
per worker in the short run and the long run.
Step by step
Solved in 7 steps with 10 images
