Question

In: Economics

Perpetual plastic plant makers cost $200 each. The number of plants that your firm expects to...

Perpetual plastic plant makers cost $200 each. The number of plants that your firm expects to produce each year for each level of capital stock is as follows:

Machines: 0 1 2 3 4 5

Plant Production: 0 250 400 500 565 600

The plants sell for $1 each and your firm faces no other costs. The real interest rate is 10% and the depreciation rate of capital is 15%. There is a 20% tax on your firm's revenues from selling these plants. Use these numbers to answer the following 4 questions: 1. What is the firm's tax-adjusted user cost of capital? 2. What is the marginal product of capital for the fourth machine? 3. How many machines should the firm buy? 4. What is the profit after deducting taxes, interest, and depreciation?

In a small open economy

Sd = $20 billion + ($100 billion)?r

Id = $30 billion - ($100 billion)?r

Y = $70 billion

G = $20 billion

r w = 0.04

5. Calculate the current account balance.

6. Calculate net exports.

7. Calculate desired consumption.

8. Calculate absorption.

A country has the per-worker production function yt = 5kt 0.5, where yt is output per worker and kt is the capital-labour ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2yt, where St is total national saving and Yt is total output.

9. What is the steady-state value of the capital-labour ratio?

10. What is the steady-state value of output per worker?

11. What is the steady-state value of consumption per worker?

Solutions

Expert Solution

Answer 2

The Third Machine Produces 500 units

The Fourt Machine Produces 565 units

So Marginal Product of 4th Machine is 565-500=65 units

Answer 1

Cost Of 1 machine =200 dollar

Interest Rate 10%= 20 dollar

Depriciation 15%= 30 dollar

So Real cost of 1 Machine= 200+20-(200-30)= 50 dollar

So Firms tax adjusted user cost of capital is 50 dollar

Answer 3

Selling Price of seed=1 dollar

Tax20%= 0.2dollar

Revenue from 1 SEED= 0.8 DOLLAR

If 2 machine are purchased then

Cost of 2 machine=2*200=400dollar

Production= 400 units

Revenue= 400*0.8=320dollar

If 1 machine is purchased then

Cost of 1 machine=1*200=200dollar

Production= 250 units

Revenue= 250*0.8=200 dollar

So Above 2 machine revenue is less than cost

Thus 1 machine needs to be purchased

Answer 4

Since the firm has purchased 1 machine

Cost Of 1 machine =200 dollar

Interest Rate 10%= 20 dollar

Depriciation 15%= 30 dollar

So purchase price of machine= 200+20=220 dollar

Selling Price of 1 machine= 200-30= 170 dollar

Revenue From1 machine= 200 dollar

Thus Profit = (170-220) + 200= 150 dollar


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