1. If the production function of an economy is 428K (1/2)L (1/2)+1167T, where T

Question

1. If the production function of an economy is 428K (1/2)L (1/2)+1167T, where T represents the amount of land, then the marginal productivity of capital ...is 214 ((L/K) (1/2)) ...gets smaller when L gets bigger. ...depends on T. 2. If the capital stock equals 200 units in year 1 and the depreciation rate is 5 percent per year, then in year 2, assuming no new or replacement investment, the capital stock would equal units. 200 210 195 190 3. If total output in the economy is 5*K(2/3)L (1/3), then the per-worker production function... ...is (5/3)(K/L) (2/3) ...will not be exceed depreciation in the steady state. ...has constant marginal productivity of capital ...is 5k (2/3)

Explanation / Answer

1. Y= 428 K1/2 L1/2 + 1167 T

Marginal product of capital is the partial derivative of Y with respect to K,

= 1/2 (428) K-1/2 L1/2

= 214 (L/K)1/2

Hence, option(A) is correct.

2. Capital stock is 200 units in year 1.

Depreciation rate = 5% per year.

Then , in year 2 , new capital stock = (200)- (200)(5%)= 200-10= 190 units.

Hence,option(D) is correct.

3. Production function, Y= 5K2/3 L1/3

Per worker production function, Y/L = (5K2/3 L1/3)/ L

y = 5 (K2/3/ L2/3)

y = 5 (K/L)2/3

   y = 5 k2/3

Hence,option(D) is correct.

4. When the capital-labor ratio is OA, AB represents investment per worker and BC represents consumption per worker. Hence, option(D) is correct.

5. Per worker production function, y=k1/3

Marginal product of capital = 1/3 (k)-2/3

= (1/3) / (k)2/3

Hence,option(A) is correct.

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