Maynard’s Cross is a trendy bistro that specializes in carpaccio and other uncooked substances. Most people who come to Maynard’s come to see and be seen by other people of the kind who come to Maynard’s. There is, however, a hard core of 10 customers per evening who come for the carpaccio and don’t care how many other people come. The number of additional customers who appear at Maynard’s depends on how many people they expect to see. In particular, if people expect that the number of customers at Maynard’s in an evening will be X, then the number of people who actually come to Maynard’s is Y = 10+.8X. In equilibrium, it must be true that the number of people who actually attend the restaurant is equal to the number who are expected to attend.
(a) What two simultaneous equations must you solve to find the equilibrium attendance at Maynard’s? __________.
(b) What is the equilibrium nightly attendance? __________.
(c) On the following axes, draw the lines that represent each of the two equations you mentioned in Part (a). Label the equilibrium attendance level.
(d) Suppose that one additional carpaccio enthusiast moves to the area. Like the other 10, he eats at Maynard’s every night no matter how many others eat there. Write down the new equations determining attendance at Maynard’s and solve for the new equilibrium number of customers. y = 11+.8x and __________.
(e) Use a different color ink to draw a new line representing the equation that changed. How many additional customers did the new steady customer attract (besides himself)? __________.
(f) Suppose that everyone bases expectations about tonight’s attendance on last night’s attendance and that last night’s attendance is public knowledge. Then Xt = Yt−1, where Xt is expected attendance on day t and Yt−1 is actual attendance on day t − 1. At any time t, Yt = 10+.8Xt. Suppose that on the first night that Maynard’s is open, attendance is 20. What will be attendance on the second night? __________.
(g) What will be the attendance on the third night? __________.
(h) Attendance will tend toward some limiting value. What is it? __________.