Question

2.2 The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: 11-10a + 2000 ($) where q is the demand and r is the unit price for this product. a Determine the maximum consumption of these consumers. b Determine the price that no consumer is prepared to pay for this product. c Determine the maximum net consumers' surplus. Explain why the consumers will not be able to realize this surplus. Fundamentals of Power System Economics d For a price π of 1000 $/unit, calculate the consumption, the consumers' gross surplus, the revenue collected by the producers, and the consumers' net surplus. e If the price π increases by 20%, calculate the change in consumption and the change in the revenue collected by the producers. f What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit. g Derive an expression for the gross consumers' surplus and the net consumers' surplus as a function of the demand. Check these expressions using the results of part d. h Derive an expression for the net con sumers' surplus and the gross consumers surplus as a function of the price. Check these expressions using the results of part d.

Answer 1

The inverse demand function of a group of consumers for a given type of widget is given by T_1 = -10q + 2000 (s) where, q = Demand pi = the unit price for this product when price is 0 we have pi = -10q + 2000 0 = -10q + 2000 q = 2000/10 therefore q = 200 When q = 0, maximum p could be Therefore pi = -10q + 2000 pi = 0 + 2000 pi = 2000 consumer surplus is area under the curve above the demand curve when the price is 0 the consumer surplus is maximum = 200 times 2000 times 0.5 = 200 times 1000 = 2,00,000 Since equilibrium price will not be zero, consumers will not be able to realize this surplus If pi = 1000 $/unit Therefore pi = -10q + 2000 1000 = -10q + 2000 10q = 2000 - 1000