Question

Consider an economy with three domestic agents: Ann, Bill and Carl

And a foreign economy with a representative agent F.

Ann owns land and uses the trees in their yard for wood. She cuts down the trees and sells the wood.

Bill owns a firm that buys wood and build and sell tables. Bill hires Carl to help him producing the tables.

There is no government.

During the year, the following transactions happened:

Ann produced and sold 1000 pounds of wood at price $10/pound.

Bill bought the 1000 pounds of wood, produced and sold 100 tables at price $500/table.

Bill paid Carl $10,000 as yearly wage.

F bought 30 tables from Bill.

The domestic agents (A, B & C) bought 70 tables from the firm owned by Bill.

There was NO depreciation of capital.

a)

What is GDP?

(you can compute it using any approach you want, but you have to explain which approach was used)

b) What is the labor share (share of labor income relative to total income)?

c) Give your answer to (b), how would you calibrate the parameter a in the production function model for this economy? Assume the Cobb-Douglas function : y=AK^(a)L^(1-a). There is no need to do any derivations for this question, just say what should be the value for a.

.

Answer 1

Answer: (a) Consumption Method:

C= 70 Tables* 500 (price) = 35000, Exports,, X= 30 Tables* 500 = 15000. Total, GDP Y = 50,000

Income Method:

GDP= All Incomes + Profits = 10,000(Carl) + 10,000 (Ann) + Profits of Bill (30,000). Hence, Y= 50,000

(b) Labour Share: Wages paid to Carl: 10,000/50,000 = 20%

(c) Hence, 1-a=0.2, hence a=0.8

Let me know if any queries.