ECON BC 3033x Lecture Notes - Lecture 3: Farad, Diminishing Returns

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olivelocust395

14 Sep 2016

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Main focus of this course is gdp. In macro, we use aggregates (ex. averages of everyone"s income) Using aggregates can mask what"s actually going on (ex. Other types of aggregates we use are inflation and price. Y=total output (in one country), y=output/person aka gdp/capita y=y/l. Assume that y is a function of labor & capital. Firms turn capital & labor consumable output. Increasing returns to scale (more than the sum of your parts) Decreasing returns to scale (less than the sum of your parts) Constant returns to scale (equal to the sum of your parts) Cobb-douglas production function + diminishing returns to scale. C(k l1- )= yc constant returns to scale. 1=constant, less than 1= decreasing, more than 1= increasing. Firms face diminishing returns to scale when firms are too small and cannot specialize. Optimal size of a firms is not one person. So there is increasing returns to scale when firm is small.

Related Questions

Suppose that an economyâs production function is Cobb-Douglas with parameter a=0.36,

and is given by

Y= AK^a L^1-a

(a) Prove that this Cobb-Douglas function has constant returns to scale.

(b) What fraction of income do capital and labor receive?

(c) Suppose that immigration raises the labor force by 20 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

(d) Suppose that a gift of capital from abroad raises the capital stock by 20 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

coffeewoodchuck539

a) Define A , K , and L

b) What does it mean that Y is proportional to A?

c) What does it mean that the marginal product of capital (MPK) and the marginal product of labor (MPL) are greater than zero? Show that the marginal products are positive in the Cobb-Douglas case.

d) What does it mean that the marginal product of capital (MPK) and the marginal product of la- bor (MPL) are decreasing? Show that the marginal products are decreasing in the Cobb-Douglas case.

e) What does it mean that the marginal product of capital (MPK) is increasing in labor? Show that the marginal product of capital increases as labor increases. Is the same true for capital?

f) Does the Cobb-Douglas production function display âconstant returns to scale?â (Doubling both inputs doubles outputs). If this is true, show it, otherwise, show it is false.

Suppose that an economy's production function is cobb-douglas with parameter Î± = 0.3

a. What fractions of income do capital and labor recieve?

b.Suppose that immigration increase the labor force by 10 percent. What happens to total output (in precent)? The rental price of capital? the real wage?

c. Suppose that a gift of capital from abroad raises the capital stock 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in perecnet)? The rental price of capital? The real wage?

For concreteness, assume that the production function is Y = 100K^0.3L^0.7and assume that the economy starts with K = 100 and L = 100. Using this information, calculate exact percentage changes for total output, the real rental rate, and the real wage rate.

ECON BC 3033x Lecture Notes - Lecture 3: Farad, Diminishing Returns

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