Assignment must be uploaded to Canvas as a single pdf file or MS Word.

It is ok to scan a hand-written document, but scan to pdf only (no jpeg or camera photo, etc.)

Note: “Briefly explain” means a sentence or two.

## 2018 U.S. GDP category or categories

**1) **

For each of the following, state which 2018 U.S. GDP category or categories (C, I, G, NX) are affected (if any) and whether 2018 U.S. GDP will rise/fall/stay the same. Briefly explain.

- Steph buys a house for $3.4 million in 2018 in Orinda, CA. The house was built in 2012.
- Klay rents a house in Oakland, CA for $5,000 a month. The house was built in 2013.
- Kevin buys a 2017 Tesla Model S for $90,000 from a dealership. The car was purchased in 2018 but had never been sold before.
- Draymond buys a meal at a restaurant, Hakkasan, in San Francisco in 2018 for $1200. The corporate headquarters for Hakkasan in London, U.K.
- San Francisco spends $55 million in 2018 to upgrade public transportation around a new sports complex being built in 2018.

**2) **TrendyVille is a hypothetical country that produces and consumes three items: avocado toast, cold brew coffee, and poke bowls. The following table represents the prices and production levels for 2017 and 2018.

**TrendyVille**

2017 | 2018 | ||||

Price | Quantity | Price | Quantity | ||

($) | (number of units) | ($) | (number of units) | ||

Avocado Toast | $7 | 5 | $8 | 7 | |

Cold Brew Coffee | $3 | 5 | $4 | 6 | |

Poke Bowl | $10 | 5 | $8 | 5 |

Using 2017 as the base year, calculate for 2018

- nominal GDP.
- real GDP.
- GDP Deflator
- Calculate the nominal growth rate of the economy between 2017-2018.
- Calculate the real growth rate of the economy between 2017-2018 using 2017 as the base year.
- Calculate the inflation rate between 2017-2018 using the GDP Deflator and the CPI.
- The GDP Deflator and the CPI are both measures of the price level, or the average level of prices. If they are both measures of the average level of prices, why are the averages we calculate different for each? Briefly explain.

### 2018 U.S. GDP

**3) **Production in the country of ECNLand can be characterized by the following function:

*Y* = 2*K*^{0.2}*L*^{0.8} and that ECNLand initially has 200 units of labor and 800 units of capital.

- Calculate the numerical value` marginal products of labor and marginal product of capital.
- Show with calculus that the production function exhibits diminishing returns to capital.
- Calculate the total payments to labor and capital in ECNLand.
- Suppose that in ECNLand there is an earthquake that destroys half the capital in the country. What happens to the rental rate of capital and real wage rate in ECNLand? Briefly explain. (You don’t need to calculate, you can just explain)
- Suppose that in ECNLand there is an earthquake that destroys half the capital in the country.

What happens to the capital’s share of income and labor’s share of income in ECNLand? Briefly explain. (You don’t need to calculate, you can just explain)

- Productivity of the workforce is often defined as Y/L. After the earthquake that destroys half the capital in the country, is ECNLandmore or less productive than before? Briefly explain.

4)** **Suppose the economy of Investoplace is seeing a change in business sensitivity to interest rates.

Currently, its economy is described by the following equations.

*Y* = 3*K*^{0.3}*L*^{0.9} *K* = 50 and *L* = 50

*G* = 60 *T* = 80

*I* = 120 – 100*r* *C* = 40 + 0.5(*Y* – *T*)

- Using math, show the returns to scale for Investoplace’s production function.
- Assuming Investoplace is a closed economy, what are the equilibrium values of consumption, investment and the interest rate?
- Suppose that Investoplace passes some new policies that cause businesses to want to invest more and this changes the investment function to
*I*= 150 – 100*r*

* *With this new investment function, solve for the equilibrium values of consumption, investment, and the interest rate.

- Sketch a loanable funds diagram for Investoplace that shows the effect of the change from part b) to part c) on national saving and investment.
- Briefly explain the economic intuition behind what is causing the result for consumption between part b) and part c).

5) In this question we are going to work through the logic of finding the steady-state in Solow Growth model. The production function is *Y* = 3*K*^{0.3}*L*^{0.7} and the saving rate is 6%, the depreciation rate is 4%, and the population growth rate is 3%

- The first step is to find the per worker production function. Divide both sides of the production function by L, then simplify the algebra. Finally, let
*y*=*Y*/*L*, and =*K*/*L*, and substitute those in.

You should end up with a function that is *y* = *f*(*k*)

- To find the steady-state we need to solve the following equation. ∆ = () − ( + ) = 0

We have *f*(*k*) from part a) and *s*, *n*, *δ* are all given. Plug in and solve for *k**, the steady-state value of *k*.

- Now that we have k*, what is y*? (plug back in to the equation from part a). Notice that
*s*f(*k*) =*i** = investment = national saving. Plug in and find*i**. Finally, notice that*c** =*y** –*i**. What is*c**? - The key to finding the Golden Rule is to solve
^{′}() = ( + )where^{′}() is the marginal product or derivative of y with respect to k. Find the function for^{′}() - Plug in to the Golden Rule equation and solve for the Golden Rule level of
*k*. - Because s is a variable with the Golden Rule, we would have to find consumption using
*c*=*y*– (*n*+*δ*)*k*.What is the Golden Rule level of consumption?