In Houston, Texas, there are 10 household each with a demand for electricity of

Question

In Houston, Texas, there are 10 household each with a demand for electricity of Q = 60 – P. Houston Lighting and Power's (HLP) cost of producing electricity is
TC = 600 + 2Q.

a. If the regulators of HLP want to make sure that there is no deadweight loss in this market, what price will they force HLP to charge. What will output be in that case? Calculate consumer surplus and HLP's profit with that price. (Answers should be rounded two decimal places)

The regulated price would be $___, and the firm would produce ___ units of electricity.

The total consumer surplus would be $___, and the firm would earn a $___ profit.

Explanation / Answer

Q = 60 - P

Or, P = 60 - Q

TC = 600 + 2Q

Marginal cost, MC = dTC / dQ = 2

(a) To ensure no deadweight loss, the market should operate as a perfectly competitive one where P = MC

So,

60 - Q = 2

Q = 60 - 2 = 58

P = 60 - Q = 60 - 58 = 2

Consumer surplus is given by area within demand curve & price.

For the demand curve P = 60 - Q, When Q = 0, P = 60 [Vertical intercept of demand curve]

So, Consumer surplus = (1/2) x (60 - 2) x 58 = (1/2) x 58 x 58 = 1,682

Profit = TR - TC

= (P x Q) - (600 + 2Q)

= (2 x 58) - (600 + 116)

= 116 - 716 = - 600 (Loss)

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