2.2 The inverse demand function of a group of consumers for a given type of widg
ID: 1147230 • Letter: 2
Question
2.2 The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: =-10q+2000[S] where q is the demand and is the unit price for this product Determine the maximum consumption of these consumers Determine the price that no consumer is prepared to pay for this product a. b. Determine the maximum consumers' surplus. Explain why the consumers will not be able to realize this surplus c. d. For a price of 1000$/unit, calculate the consumption, the consumers, gross surplus, the revenue collected by the producers and the consumers' net surplus. e. If the price increases by 20%, calculate the change in consumption and f. What is the price elasticity of demand for this product and this group of g. Derive an expression for the gross consumers' surplus and the net consumers' the change in the revenue collected by the producers consumers when the price is 1000 Sunit surplus as a function of the demand. Check these expressions using the results of part d. Derive an expression for the net consumers' surplus and the gross consumers' surplus as a function of the price. Check these expressions using the results of part d. h.Explanation / Answer
Answer:
= 10q + 2000[$]
(a) When price is zero, the q would be......
0 = -10q + 2000
10q = 2000
q = 200 (maximum consumption)
(b) maximum p could be where q = 0.
So = 10q + 2000 = 0 , = 2000.
(c) Consumer surplus is the area under the curve above the demand curve.
When price is zero, the consumer surplus is maximum = 0.5*200*2000 = 200000.
But since equilibrium price will not be zero, consumers will not be able to realize this surplus.
(d) if = 1000 $/unit, 10q = 2000 -
q = 1000/10 = 100 (consumption)
consumer surplus = 0.5*100*1000 = 50000
Revenue = P*Q = q = 1000*100 = 100 000
(e) if = 1200, 10q = 2000 -1200
q = 800/10 = 80
New TR = 80*1200 = 96000
change in TR = 4000
(f) Ep = dq/d * /q = -1/10 * 1000/100 = -1
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.