Question

Gong Li receives utility U(G,S)-G SS from her decision to consume gasoline (G) and solar power (S). Assume gasoline costs D 27 per litre, solar power costs D 16 per KWh, and her budget for energy is b 129,600 per year. The government wants consumers to change their energy consumption toward solar power, so they increase the price of gasoline to b 64 per litre. How many Dogecoins (D) do they need to offer Li to ensure that she doesn't lose utility following the price increase? (10 marks) (Be aware that I'm not just looking for a number. For full marks, you must show all your work) Now, draw Li's individual demand curve across the two prices, and solve for the own price elasticity of demand at each price. Given that you only have two points of data, assume (however incorrectly) that demand is linear. (5 marks) Solve for the change in Li's consumer surplus caused by the government's increase in gasoline price. (5 marks)

Answer 1

Given data, For calculating the equilibrium quantites demanded. The equilibrium condition is, Mv_G/Mv_s = P_G/P_s Where Mv_G & Mv_s is the marginal velocity of gasoline and solar power respectively. Mv_G = partial differential v/ partial differential G (middot) = 0.5 G^-0.5 s Mv_s = partial differential v(middot)/ partial differential s = G^0.5 0.5 G^-0.5 s/G^0.5 = 27/16 = > s/2G = 27/16 \r\n s/G = 27/8 Therefore s = 27/8 G Budget Constraint: P_G middot G + p_s middot s = Income 27 middot G + 16 middot s = 129600 Using (2) into (3) 27.G + 16 middot 27/8 G = 129600 G = 129600/81 = 1600 Therefore G*_1 = 1600 Therefore S*_1 = 27/8 times G*_1 = 5400 U(G*_1, S*_1) = squareroot 1600 middot 5400 = 216000 Therefore U(G*_1, S*_1) = 216000 The new quantities by (s*_2, G*_2) \r\n Now from equation condition, s_2/2G_2 = 64/16 = > s_2/G_2 = 64/8