Question

Question 4: In Canada, a burger restaurant named Harvey's and a chicken restaurant named Swiss Chalet compete for cold and hungry customers by choosing price (i.e. Bertrand competition with differentiated products). Since both produce food, they sell substitute products. However, their products are not identical and some consumers have a strong preference for one over the other. Suppose the demand for Harvey's is given by qH 24 - PH 0.5ps and demand for Swiss Chalet is given by qs 36 ps+0.5pH. Harvey's marginal cost per meal is 2 while Swiss Chalet's is 4 (a) Write out each restaurant's profit function. It should only depend on PH and ps. 1 (b) Find each restaurant's best response function and plot it, with pH on the horizontal axis and ps on the other (c) Solve for the equilibrium prices of each restaurant. [Involves a decimal.] (d) Why is it that the equilibrium does not have both firms pricing at their marginal cost?

Answer 1

TivenBertrand competitiern witu differerdiated preducta. odemand for Harvey'k 36- Ps + oS P Swis chalet AND Manginal fost for Harrvey (MCH) = 2 Swiss chalet (MCs)= 4 Profit function's *Harvey'z profit tunction (Pt-2) 4-P05) 24P-P 0 Pe Py- 48 2P 2 26 P Prt o. P - Ps Ч8 Soiss chalet's profit function (Ps4 (36 Ps +.5P Ps o.5 P P - 144 P - 2 PH 36 P че р. স = First order Couditien for profit maximisation of * 2PH 0.5 Ps 26- г Ри - 2PH-26- O. P best response function for Harvey 0.25 Ps н E 3 Second order Condition requires Satisfied Soc. -2 o

Foc tor profit maximisation of "s 0.S P - 2 Ps -40- 0.25 PH best respouse for SuoTss chalex P =. Soc for Prafit maximisation requires2 P 2 sSoC Latisfied) Response f best reponseffor Harvey 13 0.2-5 Ps PH= Swiss chalT 20 + 0.25 P Ps 13 25 P 0.2PH P 20 P13 S.s18 PH 20 20 Ps Ps 20 22.5 25 Py 23+02s Ps = 20 0.25P 24.8 20 13 9.2

40- (0, 20) 20 (19.2, 24.8) (13, 0) (-80, 0) 80 60 40 20 -40 0 -60 -80 20

Solve both firms best respouse tunctiong P = 13 25 Ps Ps 20 0-25 P Put. value of P from esBinto eqA 0.25(13+o 25 P) Ps 20 Ps 3.25 0. 0625 2D P- o.0625 P 2 3. 25 23 0.937 2 3.25 Ps = o.937S equilibrum pnce for Swiss chalet 24.8 put tis value into eg@ PH /3 o.25. 24.8) 13 6 2 equilibrium price for Harvey PH = 19. 2

equilibriumbethr restaurant At pricing at are net marginal cost Competing this olue to the restaurant are substitutes Foocds