Question

The French government announced plans to convert state-owned power firms EDF and GDF into separate limited companies that operate in geographically distinct markets. BBC News reported that France's CFT union responded by organizing a mass strike, which triggered power outages in some Paris suburbs. Union workers are concerned that privatizing power utilities would lead to large-scale job losses and power outages similar to those experienced in parts of the eastern coast of the United States and parts of Italy in 2003. Suppose that prior to privatization, the price per kilowatt-hour of electricity was$\mathit{n}\mathbf{0}\mathbf{.}\mathbf{13}$ and that the inverse demand for electricity in each of these two regions of France is $\mathit{P}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{35}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{002}\mathit{Q}$ (in euros). Furthermore, to supply electricity to its particular region of France, it costs each firm $\mathit{C}\mathbf{\left(}\mathit{Q}\mathbf{\right)}\mathbf{=}\mathbf{120}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{13}\mathit{Q}$(in euros). Once privatized, each firm will have incentive to maximize profits. Determine the number of kilowatt-hours of electricity each firm will produce and supply to the market, and the per-kilowatt-hour price. Compute the price elasticity of demand at the profit-maximizing price-quantity combination. Explain why the price elasticity makes sense at the profit-maximizing price-quantity combination. Compare the price-quantity combination before and after privatization. How much more profit will each firm earn as a result of privatization?

Short answer

The state regulated power firms EDF and GDF recorded losses of 120 Euros initially. After privatization they started generating a profit of $66.05euros.$

Step-by-step solution

Finding the income and marginal cost.

Given that the two state energy companies plan to separate in a market of monopolistic competition to maximize profits. The premise that marginal revenues equal marginal costs must be met in this reagd.

Marginal revenue (MR) = Marginal cost (MC)

Inverse demand function: $P=1.35-0.002Q$

Cost function for both companies:$C\left(Q\right)=120+0.13Q$

To determine the income and marginal costs, the first get the derivative of both functions. Before deriving the inverse demand function, the condition that: $TR=P\times Q$must be taken into account So,

$\begin{array}{c}TotalRevenue=(1.35-0.002Q)\times Q\\ =1.35Q-0.002Q^2\end{array}$

Now, $MR=\frac{dR}{dQ}=1.35-0.004Q$

Finding the marginal cost of energy.

The marginal cost of both energy companies can be calculated as follows:

$MC=\frac{dC}{dQ}=0.13$

Now, equating the revenue and marginal cost functions and solving for Q:

$\begin{array}{c}\text{MR}=\text{MC}\\ 1.35-0.004Q=0.13\\ 1.35-0.13=0.004Q\\ Q=1.22/0.004\\ =305\end{array}$

Thus, each firm will produce and supply to the market 305 kilowatt-hours of electricity.

Finding the price of each firm. 

To determine the price per kilowatt-hours that maximizes profit, we can substitute the obtained value of Q in the inverse demand function:

$\begin{array}{c}P=1.35-0.002\left(305\right)\\ =0.74\end{array}$

Thus, the per-kilowatt-hour price of each firm will be 0.74 Euro.

Explaining price elasticity. 

The price elasticity of demand at the profit-maximizing price-quantity combination can be calculated with the following formula

$E_{PQ}=\frac{dQ}{dP}\times \frac{P}{Q}$

$dQ/dP$ can be determinate deriving the demand function as the following:

$\begin{array}{l}\frac{dP}{dQ}=-0.002\\ E_{PQ}=\frac{1}{-0.002}\times \frac{0.74}{305}\\ E_{PQ}=-1.2131\end{array}$

The elasticity of demand of both electricity companies corresponds to the equilibrium quantity that maximizes the equilibrium of monopoly competition, must be greater than 1. The condition of profit maximization where marginal revenue equals marginal cost gives this result.

In this case, the inverse demand function is negative and so the elasticity will be inelastic. This can be verified in the monopolistic competition market because the rule that marginal income must be greater than the price does not happen here. If we substitute the value of Q in the marginal revenue function, it will give us 0.13 euro, will be less than the price of 0.74 euro.

Calculating benefits. 

We can calculate the expected benefits before and after privatization. So, we can use the profit formula to compare both scenarios:

Benefit after privatization:

$\begin{array}{c}\text{Profit}=TR-TC\\ =\left(PQ\right)-\left(120+0.13Q\right)\\ =\left(0.74\times 305\right)-\left\{120+0.13\left(305\right)\right\}\\ =66.05\end{array}$

:

Thus, profit Benefit: after privatization is 66.05 euro.

Before privatization the price of both companies was euro. So, we can substitute this value in the inverse demand function to obtain Q before privatization:

$\begin{array}{c}P=1.25-0.002Q\\ 0.13=1.25-0.002Q\\ 0.002Q=1.25-0.13\\ Q=1.22/0.002\\ =610\end{array}$

Now, we can calculate the benefit.

$\begin{array}{c}\text{Profit}=\left(0.13\times 610\right)-\left\{120+0.13\left(610\right)\right\}\\ =-120\end{array}$

Thus, firms EDF and GDF, by remaining in state ownership, recorded losses of 120 euro, while once privatized they generate a profit of $66.05$euro.