Question

A baker will supply 20 jumbo cinnamon rolls to a cafe at a price of $4.61 each. If she is offered $4.04, then she will supply 3 fewer rolls to the cafe. The cafe's demand for jumbo cinnamon rolls is given by p = D(x) = -0.6x + 8.71. What is the equilibrium point? _____ rolls at a price of $ _____ each.

Answer 1

Equation of linear supply curve: p = a + bx [where x Number of rolls, p: price]

When p = $4.61, x = 20

4.61 = a + 20b...........(1)

When p = $4.04, x = 20 - 3 = 17

4.04 = a + 17b..........(2)

(1) - (2) yields: 3x = 0.57

b = 0.19

a = 4.61 - 20b [From (1)] = 4.61 - (20 x 0.19) = 4.61 - 3.8 = 0.81

Equation of supply curve: p = 0.81 + 0.19x

In equilibrium, demand price equals supply price.

- 0.6x + 8.71 = 0.81 + 0.19x

0.79x = 7.90

x = 10

p = 0.81 + (0.19 x 10) = 0.81 + 1.9 = $2.71