Question

4. The demand equation for ACME Widgets product is given by q = 3Vy1/2 + 3ps – 2p, where • q is the monthly demand for widgets in the market, measured in 1000s of widgets. • p is the price per widget, in dollars. • p, is the average price per unit of substitutes for widgets, also in dollars. • y is the average monthly household income in the market, in $1000s. (a) (4 pts) Find the demand q, aq/ap, aq/aps and aqlay, when p = 9, ps = 10 and the average income in the market is $4000. (b) (2 pts) Suppose that the average price for widget substitutes increases to ps = 10.4, but the monthly income remains the same. Use your answer to (a) to estimate how much ACME can increase the price of widgets while keeping the demand for widgets the same as it was before. (c) (1 pts) Approximately how will this change affect the firm's monthly profit? Explain briefly.

Answer 1

We are given demand function of ACME widgets

Part(a)

when p = 10, p = 9, y = 4000 Demand for widgets, q = 26.023(000s) да др -0.345 да - +0,5187 дря 04 ду +0.00136

Part(b)

If price of substitute for widget increases from $10 to $10.4 with income remaining constant, the price of widgets must be increased from $9 to $9.6 to keep the demand for widgets same at 26023

Part(c)

Since total cost of production is not mentioned, it is assumed to be zero.So, profits are equal to the total revenue.When price of substitute for widgets changes from $10 to $10.4 with income remaining constant, price of widgets must be increased from $9 to $9.6 to keep demand for widgets constant.

On the account of this change, profits of firm increase from $234,207 (9*26023) to $249,820.8 (9.6*26023).

AND EQUATION FOR ACME WIDGETS 29 Q=3(y2 +3ps-2972 &= MONTHLY DEMAND FOR WIDGETS (1000s of widgets) P= Price per widget Ps= Average price unit of substitutes for widgets y= AVERAGE MONTHLY HOUSEHOLD Income in 1000$s2 (a) WHEN P=9 Ps= 10 y=4000 we have to find a dgovor 9 = 3C4Y2+ 3ps - 28372 9 = 3 [6000) 92+ 3(10) -269)]2 q=3[63-24 5 + 30-197€ 3(75.245) 3 (8.674) 9- 26.023 9 - 36 y 42+ 3ps-22372 o - 341)Cy* +3ps- 2.p.) (-2) aq - -3 2012 400o 0 24 -3 -0.345 63.245 +30 1. (y² + 3ps -2p) 12 At y=4000 Ps = 10 P=9 OF -(63245 +30–185v2= 60.34 5) 9=3(4¥2 +3ps -2pgY2 (+) Cy¥ +33-2pJ4-) (+2) hotele u CqYe +aps-2p)** 4.5 Cyy2 +3 ps ~ 3p9y2 y=4000 ps=10 At p=9 OR aps 4.5 (63.245 +30-182 4.5 243 +30 20 12 = - 8.674 og (+0.5187) - q = 30 y 12 + 3ps - 29/2 () CyV2 +3ps 20$" () 4) men og la Cha) could taps-polis At pag ps = 10 Ø =4000 0.75 (4000)/2 ( 400842) + 30 – 18) 2 29 = 0.75_ (63.24 5)(8.674) 0.75 Out --- 0.00136 548.5919 (b) If Ps = 10.4 INCOME REMAINS SAME AT 4060 HA WE HAVE TO FIND how mucH PRICE OF WIDGETS SHOULD BE INCREASED TO KEEP DEMAND FOR WIDGETS SAME 9=342 +385 - 227/2 26.023 = 3( 400012 + 3(10.4) – 2029/2 =) 26.023- 3(63.245 + 31.2 - 20092 -> (631245 + 31.2 - 2p3°2= 26.023 =) 194.445 -2002- 8.674 =) (941445-2p) = 75.245 94.445-75.245= 20 = 2p = 19.2 P= 9.6$ :: Price of widgets should be increased by - 0.68 to keep the demand for widgets same 1. at 26.023 when price of substitute increace from $10 to $10.4 AND INCOME REMAINS THE - SAME () TO TAL QUANTITY OF WO WIDGETS is MEASURED IN 100OS so total number of widgets produced is 26022 Price has changed from $9 to $9.6 Since cost of production is not giver assumed to be o - Profit for firm is equal to its total reve 1. Tor(92126023) = $ 234,207 Before change 7.-19.6) (26023)= $ 249,820.8 After enano Scanned with CamScanner