Chapter 1. Chapter 8 – Problem 1

Step 1

Work It Out
true
true
You must read each slide, and complete any questions on the slide, in sequence.

Question

Country A and country B both have the production function

Y = F(K, L) = K1/2L1/2.

qTAt46ktFWmeO7kAPrjcg5H5PhABC1iAhYvxZNCP6LgiRp6WL3w9Xy83rgwnoepgBdLPPIJuqSVfdR0F1HGs1ZUnV7UNo+Md2ToGE5GDJyDSxPFtTLVXc6Pe3FpkkMIzEXXMLA==

Yes, the production function has constant returns to scale. We can see this because when we increase labor and capital by the same proportion, output also increases by the same proportion. In other words, if we multiply capital and labor by the same factor, z, in the production function, K1/2L1/2, we obtain zY for output.

Question

What is the per‑worker production function, y = f(k)?

zDLDq9whX4scuoH+hjZhVrGGm0Sw22+F6cIBVDYNuvnXgLc1+CLUsOYjIrsMVnomiNKciihKmIijUaT/u0tVdxYTcSofSM3VK3qJAlPfbqB4cfCq/5CCZDFJ64wofeGAs/8CcZbn4ST9YcoMefqUiqK2MEW0XeT+rlyFxQXNDcAUOqFk7WAJElnes/GUBgvp27OmF1SU+FM4kNIdQEroWYm2isZuL2WXR8oPKE/pr/+ei+gv1jrt04u3tilfptqfCeWBtoZHJugZr+6S
Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and returns to scale and pages 206-207 in Chapter 8 for a discussion of the per-worker production function.
1:52

Step 2

Question

Country A and country B both have the production function

Y = F(K, L) = K1/2L1/2.

Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.

Country A:

k* = h4XZagboIgc=

y* = XvVM00l89Is=

c* = 6f01gzqc24U=

Country B:

k* = zhw5AiG32jY=

y* = h4XZagboIgc=

c* = KilC+r3ZaYg=

Review text pages 212-217 for a discussion of steady-state equilibrium in the Solow growth model.
3:24

Step 3

Question

Country A and country B both have the production function

Y = F(K, L) = K1/2L1/2.

Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Round your answers to two decimal places.

Country A:

y = K2wR3/CrVEc=

c = 0sdXBA03L1M=

Country B:

y = K2wR3/CrVEc=

c = Af8a/bMTV+8=

Review text pages 212-219 and Table 8-2 for a discussion of capital accumulation in the Solow growth model and details of how the economy adjusts to its steady state.

4:59