Question

Consider my utility(U) function for Q: U 60Q-30? (a) At what Q do I maximize U? (b) Graph the U function and directly below it graph my demand function for Q. (c) At the market price of PM 32, compute my: Total Utility (TU); Expenses (outlays); and Consumer Surplus (CS)

Answer 1

U = 60 Q - 3 Q^2 U is maximized when d U/d Q = 0 d U/d Q = 60 - 6 Q = 0 Q = 60/6 = 10 Therefore Q = 10 m U = p d U/d Q = m U = > p = 60 - 6 Q 6 Q = 60 - p Q = 10 - 0.17 p This is the demand equation when Q = 0, P = 10/0.17 = 60 when p = 0, Psi = 10 \r\n U = 60 Q - 3 Q^2 when Q = 0, u = 0 when Q = 10, u = 60 (10) - 3 (10)^2 = 300 Q = 10 - 0.17 p when P = 32, Q = 10 - 0.17 (32) = 4.56 T U = 60 (4.56) - 3(4.56)^2 = 211.22 Expenses = P Q = 32 (4.56) = 145.92 C S = 1/2 (60 - 32) 4.56 = 63.84