jgilberteconomics

Approach 1: Embedding the Solution

Step 2: Fill in the Cells

Now we need to enter values into the cells in the order in which they are determined. We start with the exogenous variables, filling in suitable values for income and prices. Next we fill in the values for the parameters of the utility function. All of these should be any sensible numbers, although we can use a desired solution along with knowledge of the equations to choose suitable parameter values (called calibration, the Solver example discusses this process in more detail).

Next we fill in the endogenous variable cells in the order in which they are determined. The first cell must have a closed form solution. Demand functions with Cobb-Douglas preferences are constant value shares of income. Using this fact we have closed form solutions for demand for either good, so we can directly enter both demand functions in the sheet in terms of the parameters and exogenous variables. When we are finished, hit enter and the value is displayed in the cell.

Next we can enter the expression for utility. This can be entered in terms of the previously determined quantities (cells B3 and C3). There is no need to have a closed form solution since U depends only on parameters and the demands, which in turn depend only on parameters and exogenous variables. Excel does the necessary substitutions and the value of the utility function is displayed. Change any of the underlying values and the demands/utility level will instantly be recalculated.

The last step is to create graphics. This process is the same as Step 5 for the Solver approach. The completed sheet can be downloaded here.