Some economists believe that the U.S. economy as a whole can be modeled with the

Question

Some economists believe that the U.S. economy as a whole can be modeled with the following production function, called the Cobb-Douglas production function: where Y is the amount of output, K is the amount of capital, L is the amount of labor, and A is a parameter that measures the state of technology. For this production function, the marginal product of labor is: MPL-)' Suppose that the price of output (P) is $2, A is 3, K is 1,000,000, and L is 1,000. The labor market is competitive, so labor is paid the value of its marginal product. The amount of output produced (Y) is ,and the dollar value of output (PY) is and the real vage) is ! The wage (W) is is labor compensation measured in units of output.) (Note: The wage is labor compensation measured in dollars, whereas the real wage

Explanation / Answer

Using all the given values,

a. Y = 3 * (1,000,000)0.33 (1000)0.67

Y = 3 * 95.499* 102.329

Y = 29316.9515 or this can be rounded off as 29317 units.

b. P * Y = 29317 * 2

PY = $58634.

c. VMPL = wage

VMPL = MPL * price of otuput.

VMPL = 2/3 * 3 * (1,000,000/1000)0.33 * 2.

VMPL = 19.544 * 2.

wage = VMPL = $39.089.

d. Real wage = 39.089/2

W/P = 19.544 units.

e. WL/PY = (39.089 * 1000) / 58634

WL/PY = 0.67 or 2/3

Thus option C is correct.

f. Using all of the above formulas,

The observation that the share of labour is stable, IS CONSISTENT with the given production function and scenario.

Scenario Y W W/P WL/PY P increases from $2 to $3 29317 58.632 19.544 0.667 A increases from 3 to 9 87950.85 119.724 59.862 0.68063 K increases from 1,000,000 to 8,000,000 58229.05 77.6389 38.81945 0.666668 L decreases from 1000 to 125 7278.633 77.6839 38.84195 0.667054

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