Microeconomics Elasticity of Demand Problem

Hey Germanicus, it is seemilgy reasonable to answer this question although please don't take my answer for granted as I am only a second year economic student.

I think the answer is either d or e - depending on what is given in the question, whether the demand is elastic or not. The equation I built according to your data is : Q=-200p+20,000. according to this, when there is a flooding meaning less oranges to sell, Q is miminzed, thus maximizing P because the equation has to remain equal. It is safe to say, that when there are less oranges available for sale, the price per orange is rising. so P will rise, thus making spending fall or rise - depending on the elasticity of the demand.

In my opinion the correct answer is e. I'll explain why i think so.

The idea in a nutshell: the flood makes it more costly to produce a given amount of oranges. Suppose that the market price fell. When prices go down people buy more, but the suppliers can't supply more oranges than before for less money, because their costs have gone up. So there's more demand than supply, and no equilibrium obtains.

Now let's see it formally. As lior_p wrote, the demand equation is Qd=-200*p+20000. Before the flood the supply equation is Qs1=f(p); after the flood, it is Qs2=g(p) (where f and g are some supply functions). The flood does not directly affect the demand (why should it?), so the demand equation remains the same throughout both periods.

Before the flood the equilibrium price is p', where -200*p'+20000=12000 (i.e. p'=40). We have -200*p'+20000=Qs1(p').

After the flood production costs are higher, i.e. it costs more to produce a given yield, i.e. for a given price less yield is produced, i.e. Qs2(p)<Qs1(p) for every p. The demand equation does not change, so equilibrium obtains at price p'', where -200*p''+20000=Qs2(p'').

Subtract the second equation from the first to get -200(p'-p'')=Qs1(p')-Qs2(p'') or equivalently p'-p''=200*(Qs2(p'')-Qs1(p')). Now suppose, by way of contradiction, that p''<=p', i.e. 0<=p'-p''. Then 0<=200*(Qs2(p'')-Qs1(p')) or equivalently 0<=Qs2(p'')-Qs1(p'), i.e. Qs1(p')<=Qs2(p''). Since Qs2(p'')<Qs1(p'') we get Qs1(p')<Qs1(p''). But since p''<=p', Qs1(p'')<=Qs1(p') (this is true for every supply function). A contradiction! So p'<p'', i.e. the price of oranges rises after the flood, regardless of the size of the crop failure.

 if a 1% change in price leads to a 2% change in quantity demanded, then the coefficient of price elasticity of demand is?