Question

The demand for good (Qx) is given by the following equation: Qx = 20,200 - 12.5 Px + 5 Py-M + 1.5 Ax Suppose the firm spends $3,000 per week on advertising (Ax), Px is $80, Py is $60, and income per capita (M) in the market area is $22,000. (a) Calculate the elasticity of demand for good X with respect to its own price, the price of good Y, and Income per capita. (3) (b) Calculate Qx and Px where demand for good X is unitary elastic. (3) (c) If the cost per unit of X is $60 and the firm behaves as a monopolist, calculate the elasticity of demand for good X at the profit-maximizing price.(4)
please calculate carefully

Answer 1

Ox=20200-12.58 tspy-mt Is Ax Ax= 3000 lx=80, Py=60 imo 22000 a) Elasticity with respect to Px = dax px dPX QX Qx = 20200 - 2125 (80) +5(60)–22000+1:5(3000) - 20200 - 1000 7300-22000 +4500 = 2000 elasticity of Qx with respect to Px (ex) = dax. px -12.5X So = -0.5 dex QX - 2000 2 Elasticity -0.5 Elasticity with respect to Py ley) = dox. Py sxx day QX 60 0.15 2000 Elasticity = 0.15 Elash city with respect to m (em) = dax.m= am - 1x 22000 2000 Elasticity = 11

PAG b) Demand is witaey elastic ») elocity तार कर Ox = 20,200 -12.5px +5 (60) 22000 +1:5(3000) 20,200 -12.5x + 300-22000 +45oo -12.5 Px +3000. - 12.5 JPX 25px300) dax dpx -12.5 PX -12:5RX +3000 - 12.5Px = 12.5PX - 3000 25 Rx = 3000 Px = 120 Px = 120 >> Ox= -12:5(120) +3000 = 1500 So, when demand is unitary elastic, Px= 120; Qx = 1500) c) MC 60 cost per mit Qx= 10 +2.5Px +3000 Px = 240 - Qx 12.5

PAGE Total Revenue (TR) = Px Qx = 2400 x-Qx² 12.5 MR = DIR Cox 240 2x 12.5 profit maximization of a monopolust - MRMC 60 =) 240- 20x 12.5 Qx = 180x12.5 1125. 2 Qx= 1125 = Px = 240 - 1125 12.5 150 profit maximizing price of monopolist olist is 150 Guambity is 1125. Elaestcity at profit makinining price dox fy - 12.5 x 150 wo 71.67 TIPX QX 1125 Therefore the elasticity of demand at the profit maximizing price is [-1.67