The goal of this assignment is to teach you key functionality in Excel that you will use to build the simple version of the DICE model that will form the basis for your group project. The first two exercises teach you about separating model assumptions from model equations and about copying formulas. The last exercise teaches you about posing and solving an optimization problem using the Excel Solver.
Exercise 1
In economics, a dynamic model describes how one or more variables evolve over time. The climate-economy model you will work with this semester is an example of a dynamic model. To begin to learn the Excel skills needed to build this type of model, we start with a very simple
rate 𝑔 β‰₯ 0π‘₯each time period. Build a simple excel model to simulate the path of𝑑 π‘₯ 1 0 𝑔 = 10𝑑 %= 1𝑔𝑔= 25π‘₯ π‘₯%for 𝑑 = 1𝑔 = 50, … ,%10. example.
Suppose time runs from 1 to 10. The variable equals when . grows at constant table in the template. You do not need to preserve each simulated path, only the answer to theπ‘₯ By repeating this for three different values of the growth rate ( , , and ), compute the value of in period 10 under each of these three values of . Fill in the relevant value of in the last period for each growth rate.
Exercise 2
physical infrastructure. Each period households save a constant fraction,𝐾 𝑠, of income. Since𝑠 In the simplest version of the Solow growth model, output in the economy is a function of the stock of capital, . Capital includes machines, equipment, buildings, and other forms of
households own the firms in the economy, this assumption implies that fraction of output each period gets invested into new capital. The capital also depreciates a little bit each period.
The equations of the model are 𝐾(𝑑 + 1) = π‘ π‘Œ(𝑑) + (1 βˆ’ 𝛿)𝐾(𝑑), [2.1]
1
wherewhereperiod, andin production (the percentage change in output that corresponds to a one percentage changein capital). We will assumeliterature. The function on the right side of Equation 2.2 is the production function for oursimple economy.𝛼𝛿 is a parameter in the production function that corresponds to the elasticity of capitalis the depreciation rate for physical capital and𝛼 = 0.3, which is a typical calibration value in the economicsπ‘Œ(𝑑) = 𝐾(𝑑)𝛼, 𝑠 is the constant savings rate each[2.2]
Let the period length in the model be a year, so the parameters should correspond to annual values. A plausible annual value for the depreciation rate of capital is 10% per year. Further assume that the economy (through households) saves 25% of output each year.
Using these parameters, along with Equations 2.1 and 2.2, simulate the trajectory of capital and output in the economy over 50 years. Plot output as a function of time, and explain in
words (under the graph in your spreadsheet) what happens to economic growth in the model.Assume that the initial value of capital in the first period isperiod output is alsoin the initial period. 1.0, so output in subsequent periods can be viewed as a multiple of output1.0. Under this assumption, initial
The next exercise will require you to use the Excel Solver. You should work through one or more tutorials on this topic before you attempt it.
Exercise 3
The price of soda isYou and your roommate go to the movies. You have a $10 gift card to spend on soda andYour utility maximization problem is thus given by:quantity of soda that you buy andpopcorn. Since it is a gift card, it is in your best interest to spend all of it. Let𝑝𝑠 = $1 per unit, the price of popcorn is𝑃 the quantity of popcorn. Your utility is given by:π‘ˆ(𝑆, 𝑃) = 𝑆𝛼𝑃1βˆ’π›Ό. 𝑝𝑝 = $2, and the parameter𝑆 denote the𝛼 = 0.5.
To solve this problem, we will use Excel’s Solver tool to numerically compute the optimaland . The three key ingredients to any Solver optimization problem are:subject to max𝑝𝑆,𝑃𝑠𝑆 𝑆+𝛼𝑝𝑃𝑝1βˆ’π‘ƒπ›Όβ‰€ 10.
What is the optimal quantity of popcorn and soda for you to buy? What fraction of yourbudget do you spend on popcorn? The Excel template for the exercise will help you get started.choice of1.3.2. The target cell = Our objective function (The changing cell(s) = Our choice variables (The constraints =𝑆 𝑃 [𝑝𝑠𝑆 + 𝑝𝑐𝐢 ≀ 10] π‘ˆ(𝑆, 𝑃𝑆, 𝑃) =) 𝑆𝛼𝑃1βˆ’π›Ό)
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