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You are asked to consider the following scenario. Let the demand for a good be givenas(QD − Q0) = −βD(PC − P0),where QD is the demanded quantity, Q0 > 0, P0 > 0 are constants, and βD ≥ 0 is thenegative of the slope of the demand curve and PC is the consumer price (PC = P +t).The supply is given by(QS − Q0) = βS(P − P0)where, QSis the quantity supplied, BS ≥ 0 is the slope of the supply curve and P isthe producer price. 1
(a) Solve for the equilibrium quantities P and Q as functions of the parameters(constants in the problem) when the tax rate is t = 0.
(b) Let Q0 = 5, P0 = 5. Draw the market equilibrium when (βD, βS) are (1, 1),(0, 1) and (∞, 1). For the last one consider this as the limit case when βD growswithout a bound, meaning when the demand curve becomes horizontal
(c) Suppose the government introduces a tax at a rate t > 0. Solve for the equilibriumprices and quantities. Draw the figures for the same values of the betas asin the part(b) for t = 1. Identify the deadweight loss of tax and tax revenue inthese figures.
(d) Using your answer in the previous part derive expressions for P(t), PC(t) andQ(t), i.e. the equilibrium producer price, the consumer price and the quantityas functions of the tax rate t. Note that this question is for a general values ofthe parameters.
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