excel

Model

Electricity pricing model
Input data					Range names used:
Coefficients of demand functions					Capacity	=Model!$B$15
	Constant	On-peak price	Off-peak price		Common_Capacity	=Model!$B$21:$C$21
On-peak demand	2.253	-0.013	0.003		Demands	=Model!$B$19:$C$19
Off-peak demand	1.142	0.005	-0.015		Prices	=Model!$B$13:$C$13
					Profit	=Model!$B$26
Cost of capacity/mWh	$75
Decisions
	On-peak	Off-peak
Price per mWh	$137.57	$75.85
Capacity (millions of mWh)	0.692
Constraints on demand (in millions of mWh)
	On-peak	Off-peak
Demand	0.692	0.692
	<=	<=
Capacity	0.692	0.692
Monetary summary ($ millions)
Revenue	147.712
Cost of capacity	51.908
Profit	95.804

Although this is a small model, it is sufficiently complex to defy an intuitive solution. Both of the prices drive demands for both periods, not just their own, and these demands drive the capacity decision. By lowering prices, demands increase, which means more capacity is needed. By increasing prices, there is less demand, which means less capacity is needed. But in either case, it is difficult to guess the net effect on profit (without doing the calculations). This is a good model to demonstrate why the optimal policy is optimal once you know it, as we did in the book. That is, you can follow the chain of changes that would occur if, say, we increased the peak-load price from $137.57 to a slightly larger (or smaller) value. The net effect should be a decrease in profit.

Model_STS

1
$B$9
1
60
80
2
$B$13:$C$13,$B$15,$B$26
Cost of capacity

STS_1

Oneway analysis for Solver model in Model worksheet										Sensitivity of Prices_1 to Cost of capacity
Cost of capacity (cell $B$9) values along side, output cell(s) along top										Data for chart
	Prices_1	Prices_2	Capacity	Profit					1	Prices_1
$60	$133.82 Chris: Solver converged in probability to a global solution.	$72.10	0.730	106.466						133.82
$62	$134.32 Chris: Solver converged in probability to a global solution.	$72.60	0.725	105.012						134.32
$64	$134.82 Chris: Solver converged in probability to a global solution.	$73.10	0.720	103.568						134.82
$66	$135.32 Chris: Solver converged in probability to a global solution.	$73.60	0.715	102.134						135.32
$68	$135.82 Chris: Solver converged in probability to a global solution.	$74.10	0.710	100.710						135.82
$70	$136.32 Chris: Solver converged in probability to a global solution.	$74.60	0.705	99.295						136.32
$72	$136.82 Chris: Solver converged in probability to a global solution.	$75.10	0.700	97.891						136.82
$74	$137.32 Chris: Solver converged in probability to a global solution.	$75.60	0.695	96.497						137.32
$76	$137.82 Chris: Solver converged in probability to a global solution.	$76.10	0.690	95.113						137.82
$78	$138.32 Chris: Solver converged in probability to a global solution.	$76.60	0.685	93.738						138.32
$80	$138.82 Chris: Solver converged in probability to a global solution.	$77.10	0.680	92.374						138.82

Sensitivity of Prices_1 to Cost of capacity

60 62 64 66 68 70 72 74 76 78 80 133.82 134.32 134.82 135.32 135.82 136.32 136.82 137.32 137.82 138.32 138.82

Cost of capacity ($B$9)

When you select an output from the dropdown list in cell $K$4, the chart will adapt to that output.

Do these results make sense intuitively? You can be the judge. As capacity gets more expensive, less of it is used, and profit decreases. Both of these make sense. But the on-peak and off-peak prices both increase. Why?

image1.png

image2.png