step_2

Approach 2: Using Solver

Step 2: Fill in the Cells

Next we enter values for the exogenous variables (the white cells). The values aren't important except that they should be economically meaningful. Usually, it is a good idea to normalize all prices to unity, thus making any value term a quantity term. Once the exogenous variables are entered, we enter values for the endogenous variables (the grey cells). These will be the starting point, and ideally we want them to be a solution to the problem. At this stage this means that the basic accounting in the model must be sound (i.e., the total value of consumption should be equal to income):

Now we need to enter the equations. In cell C3 we type "=B7*B11/P5", the demand function for good X with Cobb-Douglas preferences. At this stage cell C3 will contain a zero value. We do the same for consumption of Y in cell E3:

Now we calibrate the model so that our choices for the values of the endogenous variables are in fact a solution. With Cobb-Douglas preferences, the exponents are the value shares of income. Hence, we enter =100/200 in cells B11 and D11. Note that when we enter these values, the cells C3 and E3 change to equal the value in the cell to the immediate left. This indicates that we have calibrated that section of the model correctly. Note also that we do not use =B3/B7 to set the value in C3, the reason being that the variable cells change their value in response to changes in exogenous variables or parameters, and we want the parameters to be a fixed number. The utility shift parameter in B13 is set in the same way, using the underlying utility function. Again, the value here must be a number, not a function.

Finally, we replace the value that we had for utility in cell B9 (our target for calibration) with the actual utility function, expressed in terms of the endogenous variables and our calibrated parameters. This cell will be a objective function. When entered, the value in the cell should be 200, if we have correctly calibrated:

<Step 1> <Step 2> <Step 3>