How would I find the equilibrium point?

Question

A baker will supply $22$ jumbo cinnamon rolls to a cafe at a price of $4.63$ dollars each. If she is offered $\$3.87$, then she will supply $4$ fewer rolls to the cafe. The cafe's demand for jumbo cinnamon rolls is given by $p = D(x) = -0.25x + 6.17$. What is the equilibrium point?

The answer was $13$ rolls sold at $\$2.92$ each

What would I do to find the answer to this? I tried $4.36 = -0.25 \cdot 22+b$ and $3.87 = -0.25 \cdot 19+b$ but it isn't working out so I'm not quite sure. Please comment any questions, thanks!

score 1 · Answer 1 · answered Nov 07 '17 at 19:48

1

hint

You use the first condition (and the unspoken assumption that the supply function is linear) to write a linear supply function $S(x).$ You are given two points $(18,3.87)$ and $(22,4.63)$ so you can determine this line. Then just set $S(x)=D(x)$ and solve for $x.$

answered Nov 07 '17 at 19:48

spaceisdarkgreen

58,508

would I do ($3.87-4.63)/(19-22) then (x-22)+(4.63) ? – Kevin Diez Nov 07 '17 at 23:26
That first expression gives the slope $m=0.19$ and then the supply curve is $S(x) = m(x-22) + 4.63.$ – spaceisdarkgreen Nov 08 '17 at 00:37

How would I find the equilibrium point?

1 Answers1