This probably belongs in the Business Math section.
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
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
I assume you're stuck on part (b), which is the first part involving elasticity.
(a)
Equilibrium: Demand = Supply
QD=QS
24-3PC=15+6PP
You're told that PC=PP
24-3P=15+6P
Solve for P. Use the demand function to get QD. Now you have the equilibrium price (P=PC=PS) and quantity (Q=QD=QS)
(b)
Use the elasticity formula, which you should look up. from memory i think it is:
comes from differentiating the demand function, and you just calculated the values of PC and QD.
if you already compued Sε [which i assume is your notation for price elasticity of supply] then thats the answerin part c/ I use the Dε and Sε of part b
no, for (d) you'll need to find the new equilibrium price and quantity, and the new elasticities at that equlibrium. Use those with the formulae provided.in part d/ I use the Dε and Sε of part b
Your answer to (d) will tell you which price responds most to changes in tax. Its an elasticity question....so the reason probably has something to do with that, see if you can work it out.how to solve e/
all of the above comes with an "I think" caveat as i haven't actually seen the formulae in part d before.