Question

The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: 2.2 π=-104 + 2000 (S)
2.3 2.4 and 2.5 Economists estimate that the supply function for the widget market is given by the following expression: 2.3 4-0.2--40 a Calculate the demand and price at the market equilibrium if the demand is as defined in Problem 2.2 b For this equilibrium, calculate the consumers gross surplus, the consumers net surplus, the producers revenue, the producers profit, and the global welfare. 2.4 Calculate the effect on the market equilibrium of Problem 2.3 of the following interventions: a A minimum price of $900 per widget b A maximum price of $600 per widget c A sales tax of $450 per widget. In each case, calculate the market price, the quantity transacted, the consumers net surplus, the producers profit, and the global welfare. Illustrate your calcula tions using diagrams. Calculate the deadweight loss compared to the results of Problem 2.3. Summarize your results in a table and discuss briefly 2.5 The demand curve for a product is estimated to be given by the expression: q 200-π Calculate the price and the price elasticity of the demand for the following values Repeat these calculations for the case where the demand curve is given by the of the demand: 0, 50, 100, 150, and 200. 10000
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Answer #1

2.3 a) Equilibrium condition; Demand = Supply

- 10q + 2000 = 5q + 200

15q = 1800

q = 120

P = 5(120) + 200 = 800

b) C.S = 1/2 x (2000 - 800) x 120 = 72000

P.S = 1/2 x (1800 - 200) x 120 = 36,000

Producer revenue = PQ = 120 x 800 = 96,000

Global surplus = C.S + P.S = 108,000

2.4 Maximum price means price ceiling while minimum price means price floor.

Under price floor, there is excess supply of good because floor is set above equilibrium price of market.

Under price ceiling, there is excess demand of good because ceiling is set below equilibrium price of market.

Sales tax increases the cost of firm and thus supply of good decreases which shifts supply curve leftwards and causing dead-weight loss.

Dern and 20000 0 12o At p = 900 P. + 요.DOO 0100 Domand Ito 0 *^Bo eioht

5 pwレ P. At P- 6o0 ut 2000 -80o

c) Sales Tax S+ Qw 139.= 1350 0 o500 Global weshoe 012Stb 2. 63S๖

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