Consider the market for widgets. The quantity of widgets demanded by consumers is

QD = 24 − 3PC ,

and the quantity of widgets offered by suppliers is given by the function

QS = 15+6PP ,

where QD and QS are the quantity of widgets demanded and supplied, respectively, and PC and PS are the consumers’ and producers’ prices. The relationship between consumers’ and producers’ prices can be defined by the function PC = PP +T, where T denotes a tax.

(a) Assume, initially, that there is no tax so that PP = PC = P . What is the

equilibrium price and quantity in the widget market?

(b) Assuming that Dε < 0, determine the elasticity of demand at the original

equilibrium price and quantity. ( denotes the elasticity.)

(c) Assuming that Sε> 0, determine the elasticity of supply at the original equilibrium price and quantity.

(d) Now assume that a tax of T = 0.3 has been levied on widget production.

Determine the impact that a change in T has on producers’ prices with the formula

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Determine the impact on consumers’ prices with the formula

(e) Which price, PC or PP , responds more to the increase in T? Why? Calculate

the new equilibrium quantity, consumers’ price, and producers’ price