Question

3. (8 points total) Suppose a firm has the following benefit and cost structure: B(O) 1400-302 C(Q) 0.5Q2 a. Find the MB(Q) and MC(Q) functions. b. What value of Q maximizes the Net Benefit NB(Q)-B(Q)-C(Q)? (50 points total) Abby is a first grader who likes to drink milk and juice. Sup her $12 a week in pocket money to spend only on milk and juice. Suppose . $1.50 and the price of juice is $2 a. b. c. Write down her budget set in algebraic (equation) form. Write down her budget line in algebraic (equation) form Draw her budget line or constraint on a graph where the number is on the X-axis and the number of milk boxes she buys is on the Y

How do I find the functions for MB(Q) & MC(Q). Plus I’m looking for the value of Q that maximizes the Net Benefit NB(Q)=B(Q)-C(Q)?

I’m looking for help directly on #3 a.) and b.)

Answer 1

B(Q) = 140Q - 3Q^2 Differentiate B(Q) w.r.t Q in order to get MB(Q) MB(Q) = partial differential B(Q)/partial differential Q MB(Q) = 140 - 3(2)Q MB(Q) = 140 - 6Q rightarrow C(Q) = 0.5 Q^2 Differentiate C(Q) w.r.t Q in order to get MC(Q) MC(Q) = partial differential C(Q)/partial differential Q MC(Q) = (0.5) (2) Q MC(Q) = Q NB(Q) = B(Q) - C(Q) NB(Q) = 140Q - 3Q^2 - 0.5Q^2 NB(Q) = 140Q - 3.5Q^2 Foc: Differentiate NB(Q) w.r.t Q and put it equal to zero. partial differential NB(Q)/partial differential Q = 140 - 3.5 (2) Q = 0 \r\n = > 140 - 7Q = 0 = > 7Q = 140 Q = 140/7 Q = 20 rightarrow critical value Soc: partial differential^2NB(Q)/partial differentialQ^2 = -7 < 0 Since, partial differential^2NB(Q)/partial differential Q^2 is negative, implies that critical value Q = 20 will maximize the Net Benefit.