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Market in competitive equilibrium, the demand is the demand and supply respectively are p = 100...

Market in competitive equilibrium, the demand is the demand and supply respectively are p = 100 - QD and p = 20 + (QS /3). The government introduces a subsidy of s = $4 per unit of the good sold and bought Suppose the government is trying to determine the amount of subsidy (they think they can do better than s=$4), to maximize the equilibrium quantity transacted (bought and sold) in the market, yet it has a budget of $1500 to spend on the subsidy provision. What is the maximum quantity the government subsidy can induce, and what is the amount of subsidy per unit to achieve this?

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