Using a linear regression equation, assume that the estimated demand function is given by:

\[ E = 2400 - 25p + 84F \]

where \( E \) is residential energy consumption in gigawatt-hours (GWh), \( p \) is the price in cents per kilowatt-hour (KWh), and \( F \) is the temperature in Fahrenheit degrees.

1. Estimated Residential Electricity Demand:

What is the estimated residential electricity demand if the price is 8¢ per KWh and the average monthly temperature is 80 degrees?

2. Price Elasticity of Demand:

What is the price elasticity of demand? Is the demand elastic or inelastic?

3. Temperature Variable Sign:

In Florida, electricity use rises with temperature because air conditioning is a significant source of demand. What sign would you expect on the temperature variable in Canada and the northern U.S. states? Explain.

If the price is 8¢ per KWH and the average monthly temperature is 80 degrees, the estimated residential electricity demand can be calculated using the given demand function as follows:

E = 2400 - 25p + 84F
E = 2400 - 25(8) + 84(80)
E = 2400 - 200 + 6720
E = 6920 GWh

The price elasticity of demand can be calculated using the formula:

Price elasticity of demand = (% change in quantity demanded) / (% change in price)

Assuming a small change in price from 8¢ to 9¢ per KWH, the % change in price would be:

% change in price = (9 - 8) / 8 * 100% = 12.5%

Using the demand function, the % change in quantity demanded can be calculated as:

% change in quantity demanded = (E2 - E1) / E1 * 100%
% change in quantity demanded = (2400 - 25(9) + 84(80) - 2400 + 25(8) - 84(80)) / (2400 - 25(9) + 84(80)) * 100%
% change in quantity demanded = 5.36%

Therefore, the price elasticity of demand is:

Price elasticity of demand = 5.36% / 12.5% = 0.43

Since the price elasticity of demand is less than 1, the demand is inelastic. This means that a change in price will have a relatively small effect on the quantity demanded.

In Canada and the northern U.S. states, the sign on the temperature variable would likely be negative. This is because as the temperature decreases, the demand for heating increases.

However, the effect of heating on electricity demand is much smaller than the effect of air conditioning, so the temperature variable would likely have a smaller coefficient in the demand function.

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