Question

Market equilibrium Consider the demand function of tofu given by Qd = 150 – 10p + 5pb and the supply function of tofu given by Qs = 50 + 20p – 7ps, where pb is the price of beef and ps is the price of soybeans. a) Find the equilibrium price (pe) and quantity (Qe) of tofu, in terms of the beef price (pb). Consider the average soybean price to be ps = 2 $/lb. b) Calculate pe and Qe when beef price is pb = 5 $/lb. c) If the price of tofu is fixed at @ 2.5 $/lb, will the market have excess demand or excess supply? Explain. d) The willingness to pay for tofu increased significantly after the Plant-Based Burger Battle organized in Davis. The new demand is given by Qd = 180 – 10p + 5pb). Keeping the same supply function, what are the new pe and Qe? (Consider the same pb = 5 $/lb and ps = 2 $/lb.)

Answer 1

a) Qs = 50 + 20p - 7ps

= 50 + 20p - 7×(2)

= 50 + 20p - 14

= 36 + 20p

At equilibrium,
`Q_(d)` =
`Q_(s)`

So, 150 - 10p + 5
`p_(b)` = 36 + 20p

So, 20p + 10p = 30p

= 150 - 36 + 5
`p_(b)`

= 114 + 5
`p_(b)`

So, p = (114/30) + (5/30)
`p_(b)`

= 3.8 + 0.17
`p_(b)`

Thus,
`p_(e)` = 3.8 + 0.17
`p_(b)`

Q = 36 + 20p

= 36 + 20(3.8 + 0.17
`p_(b)`)

= 36 + 76 + 3.4
`p_(b)`

= 112 + 3.4
`p_(b)`

Thus,
`Q_(e)` = 112 + 3.4
`p_(b)`

b)
`p_(e)` = 3.8 + 0.17
`p_(b)`

= 3.8 + 0.17×(5)

= 3.8 + .85

= 4.65

`Q_(e)` = 112 + 3.4
`_(b)`

= 112 + 3.4(5)

= 112 + 17

= 129

c) Qd = 150 - 10p + 5pb = 150 - 10(2.5) + 5(5) = 150 - 25 + 25 = 150

Qs = 36 + 20p = 36 + 20(2.5) = 36 + 50 = 86

Thus, there is excess demand as
`Q_(d)` >
`Q_(s)`

d) New
`Q_(d)`= 180 - 10p + 5
`p_(b)`

= 180 - 10p + 5×(5)

= 180 - 10p + 25

= 205 - 10p

Now, new
`Q_(d)` =
`Q_(s)` gives,

205 - 10p = 36 + 20p

So, 20p + 10p = 205 - 36

So, 30p = 169

So, p = 169÷30

So,
`p_(e)` = 5.63

Q = 205 - 10p = 205 - 10×(5.63) = 205 - 56.3 = 148.7

So,
`Q_(e)` = 148.7