Question

1. Estimate Demand

a. Suppose you are given this information from a consumer making rational, optimized decisions. Sketch a graph of demand for “theater movies” using the available data.

Price Quantity Price of of : «พื้ @พื้ of Quantity Theater Home Theater of Home Budget Movies Videos MoviesVideos 100 100 100 100 20 15 10 2 2 2 2 25 25 25 25 8

b. Estimate the linear demand curve (i.e., ??? = ? + ????) for “theater movies” that best approximates the data and add it to your graph.

c. What is the point (price and quantity) at which demand is “unit elastic”?

Answer 1

(a) Graph as follows.

(b) Using regression analysis, summary output as follows.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9113
R Square	0.8305
Adjusted R Square	0.7457
Standard Error	1.1916
Observations	4
ANOVA
	df	SS	MS	F	Significance F
Regression	1	13.91027088	13.91027	9.7969	0.088702061
Residual	2	2.83972912	1.419865
Total	3	16.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	9.2686	1.5618	5.9347	0.0272	2.5489	15.9883
Price	-0.3544	0.1132	-3.13	0.0887	-0.8416	0.1328

Estimated linear regression:

Price (P) = 9.2686 - 0.3544 x Quantity demanded (Qd)

(c) From demand function,

Qd = (9.2686 - P) / 0.3544

Point elasticity (E) = (dQd/dP) x (P/Qd) = -(1/0.3544) x [P / {(9.2686 - P) / 0.3544}]

E = - (1/0.3544) x [0.3544P / (9.2686 - P)]

E = - P / (9.2686 - P)

When demand is unit elastic, E = -1.

- P / (9.2686 - P) = -1

P / (9.2686 - P) = 1

P = 9.2686 - P

2P = 9.2686

P = 4.6343

Qd = (9.2686 - 4.6343) / 0.3544 = 4.6343 / 0.3544 = 13.0765