Question

To celebrate their Queen’s 90^th birthday, the country of Wonderland has decided to bake the world’s largest cake. The main ingredient of the cake will be flour. It has been estimated that the cake will use 50,000 tons of flour, which represents 20% of the current supply of flour. The current price of flour is $4000 per ton. Previous study has shown the elasticity of supply, ε_s, for flour to be 0.3 and the elasticity of demand, ε_d to be -1.2.

a. Assuming linear demand curves, what is the percentage change in the price of flour you would anticipate as a result of this project? What do you expect to be the change in quantity supplied as well as the change in quantity demanded by private consumers? What is the opportunity cost of flour that you would use in a cost-benefit analysis of this project?

[Hint: Es = (ΔQs/ΔP)(P/Qs) and Ed =(ΔQd/ΔP)(P/Qd) where Qs is current supply and P is current price.

Note that the amount of flour demanded by the project Qp = ΔQs – ΔQd]

b. Sketch the supply and demand for flour and show the opportunity cost on your sketch.

Answer 1

Sol :

(a) Linear Demand Curves menas graphical representation of relationship between demand of the goods and price of the goods.

elasticity of supply (Es) = (ΔQs/ΔP)(P/Qs)

                          0.3 = (ΔQs/ΔP) ( 4000/250000)

                        0.3/.016 = (ΔQs/ΔP)

                        18.75 = ΔQs/ΔP                            ..........................................(1)

elasticity of demand (Ed) = (ΔQd/ΔP)(P/Qd)

             1.2 = (ΔQd/ΔP)(4000/50000)

             1.2/0.08 = (ΔQd/ΔP)

              15 = (ΔQd/ΔP)                                       .............................................(2)

Amount of flour demanded by the project = Qp = ΔQs – ΔQd

                                                                     50000 + ΔQd = ΔQs                   .................................... (3)

                                                                         Putting of the value obtained in (3) in (1)

     18.75 = ΔQs/ΔP  

where , 50000 + ΔQd = ΔQs

18.75 = (50000 + ΔQd ) / ΔP  

ΔP   = (50000 + ΔQd ) / 18.75                                                 .....................................(4)

                                                                         Putting of the value obtained in (4) in (2)

15 = (ΔQd/ΔP)   

15 = (ΔQd / (50000 + ΔQd ) / 18.75 )

15 = ( (ΔQd ) x 18.75 ) / (50000 + ΔQd )

15 x (50000 + ΔQd ) = 18.75 (ΔQd )

750000 + 15(ΔQd ) = 18.75(ΔQd )

750000 = 3.75(ΔQd )

750000/3.75 = (ΔQd )

200000 = (ΔQd )                                                ......................................(5)

(i) ΔP = (50000 + ΔQd ) / 18.75    

           = (50000 + 200000) / 18.75

          = 250000/18.75

        = 13333

percentage change in price = (13333/4000)*100

                                              = 333.325 %

(ii)change in Quantity Supplied = 18.75 = ΔQs/ΔP  

                                    = 18.75 = ΔQs / 13333

                                    = 18.75 x 13333

                                ΔQs = 249993.75

(iii) Change in Quantity Demanded = ΔQd = 200000

(iv) opportunity cost of flour = there will be no opprtunity cost , as there is no alternative present for the flour.

as , formula for calculation of opportunity cost is = ΔY (loss of unit Y) / ΔX (Gain of unit X)

since, only one goods is given (i.e Flour) , so , we cannot calculate Opportunity cost.

(b) Sketch for Inelastic demand and elastic supply curve is as follows :