Question

4. Suppose you can hire a mechanic to work on your car for up to six hours. The total benefit of repair work is B(H)-100H-5H2 and the total cost is C(H) = 10H + 5H2, where H is the number of hours. (a) What is the net benefit? (b) Graph the net benefit function from 0 to 10 hours (c) What is your marginal benefit? (d) What is your marginal cost? (e) Graph marginal benefit and marginal cost curves from 0 to 10 hours on the same graph (f) What is your choice that maximizes the net benefit? (g) What is the total benefit at the optimal choice? (h) What is the total cost at the optimal choice? (i) What is the net benefit at the optimal choice?

Answer 1

The total benefit is B(H) = 100H -5H and total cost is C(H)=10H +5H? Here. H is the number of hours. Find the net benefit. Net benefit is the difference between benefit and cost. NB(H)= B(H)-C(H) = 100H -51° -10H-5H2 = 90H -10H Thus, net benefit is 90H -10H? (b) Graph the net benefit from 0 to 10 hours. Net benefit Net benefit 8 10 12 Number of hours The blue curve represents the net benefit curve.

Derivate the benefit function with respect to H. MB(H) = ABCH) = 100-107] Thus, marginal benefit is 100-101 (d) Derivate the cost function with respect to H. MC(H)-4C(H) 2= 10+10H ΔΗ Thus, marginal cost is 10+10H The following graph is showing the marginal benefit and marginal cost. MB and MC Costs 8 10 12 6 Number of hours marginal benefit marginal cost Blue line represents the marginal benefit and orange line represents the marginal cost. Derivate the net benefit function to get the optimal hour where the net benefit maximizes and equate it equal to 0.

ANB(H) -90-20H = 0 ΔΗ 20H = 90 H = 20 = 14,5 Thus, 4.5 hours where the net benefit maximizes. Find the total benefit at 4.5 hours. B(H)=100(4.5) - 5(4.5)? =450-101.25 = 348.75 Thus, total benefit is 348.75

C(H)=10(4.5)+5(4.5)2 = 45 +101.25 = 146.25 Net benefit is the difference between the total benefit and total cost Net benefit = 348.75 - 146.25 = 202.5