# Practice Problems (Module 2) – ECO 202

Question #1: Total output within the 50 states is 2400 in a year when the total income of american workers and firms is 3500. American workers and firms produced 1500 abroad. How much did foreign workers and firms produce in the US?

A) 1800
B) 400
C) 700
D) 1200

A) 1800
B) 400
C) 700
D) 1200

We're looking for foreign production within the US.

While we don't have a defined equation for this value, we can use the GNP formula to solve!

GNP = GDP - Foreign output in US + US output abroad

Now, let's go through the question and pinpoint variable values within this question so that we can solve for Foreign output in US.

We can pinpoint a GDP value of 2400 here...

Question #1: Total output within the 50 states is 2400 in a year when the total income of american workers and firms is 3500. American workers and firms produced 1500 abroad. How much did foreign workers and firms produce in the US?

GNP = 2400 - Foreign output in US + US output abroad

...and a US output abroad value of 1500 here...

Question #1: Total output within the 50 states is 2400 in a year when the total income of american workers and firms is 3500. American workers and firms produced 1500 abroad. How much did foreign workers and firms produce in the US?

GNP = 2400 - Foreign output in US + 1500

...and lastly, a GNP value of 3500 here.

Question #1: Total output within the 50 states is 2400 in a year when the total income of american workers and firms is 3500. American workers and firms produced 1500 abroad. How much did foreign workers and firms produce in the US?

3500 = 2400 - Foreign output in US + 1500

When we solve...

3500 = 2400 - Foreign output in US + 1500
3500 = 3900 - Foreign output in US
-400 = -Foreign output in US
Foreign output in US = 400

...this results in a Foreign output in US value of 400, which corresponds to answer choice B!

A) 1800
B) 400
C) 700
D) 1200

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

We're given the equation for potential output here:

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

Yp = 5 * L1/2 * K1/2

This means that we need to solve for L and K...

Yp = 5 * L1/2 * K1/2

...and then plug them into this equation to find our potential output!

### Finding L

We'll solve L by setting these two equations equal to each other.

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

For full clarity: we're setting these equations equal to each other because they represent the supply & demand of labor in the economy. Therefore, by setting them equal to each other, we're able to find the equilibrium labor (L) value that will exist in this economy!

300 - 2L = -132 + 1L

When we solve for L...

300 - 2L = -132 + 1L
300 = -132 + 3L
432 = 3L
L = 144

...we get a value of 144!

Let's plug this into our potential output equation like so:

Yp = 5 * (144)1/2 * K1/2

Moving onto solving for K...

### Finding K

We'll solve for K with the following equation:

K (This Year) = K (Last Year) + Gross Investment - Depreciation

Based on the question, K (Last Year) was 110...

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

K (This Year) = 110 + Gross Investment - Depreciation

...and Gross Investment is 40...

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

K (This Year) = 110 + 40 - Depreciation

...and Depreciation is 6.

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

K (This Year) = 110 + 40 - 6

This results in a K (This Year) value of 144!

K (This Year) = 110 + 40 - 6
K (This Year) = 144

Let's plug this into our potential output like so:

Yp = 5 * (144)1/2 * (144)1/2

### Solving for potential output

Now that we've got L and K plugged into our potential output equation, we can solve like so!

Yp = 5 * (144)1/2 * (144)1/2
Yp = 5 * 12 * 12
Yp = 720

This results in our final answer!

Question #3: In the previous question, if the real wage was 1.2, what was the price level in this economy?

To solve this problem, we must first understand the formula for the real wage.

Real Wage = Wages / Prices

You may see this abbreviated as...

Real Wage = W / P

In the case of this problem, we're trying to solve for Prices.

Real Wage = Wages / Prices

The problem tells us that Real Wage equals 1.2...

1.2 = Wages / Prices

...so all we need to do is plug in a value for Wages to solve for Prices!

If you recall, in Question #2 the labor functions both solved for Wages (W)!

Question #2: The productions function in Oxford is Yp = 5L1/2K1/2. Capital stock last year was 110. There was new investment of 40 and depreciation of 6. Also, labor demand is given by W = 300 - 2Ld, while labor supply is given by W = -132 + 1Ls, where W is the real wage rate. What is the value for potential output?

And, in Question #2 we identified a labor (L) value of 144...

300 - 2L = -132 + 1L
300 = -132 + 3L
432 = 3L
L = 144

...therefore, to solve for Wages (W) all we need to do is plug L = 144 into either of these wage functions (they'll return the same thing).

Labor Demand
W = 300 - 2(144)

Labor Supply
W = -132 + 1(144)

When we solve...

Labor Demand
W = 300 - 2(144)
W = 300 - 288
W = 12

Labor Supply
W = -132 + 1(144)
W = -132 + 144
W = 12

...we get a Wages (W) value of 12!

Let's plug that into our Real wages equation like so:

1.2 = 12 / Prices

Now, we can solve for Prices like so...

1.2 = 12 / Prices
1.2 * Prices = 12
Prices = 12 / 1.2
Prices = 10

...resulting in a final answer of 10!